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<span class="vector-toc-numb">5</span> <span>Visualization</span> </div> </a> <ul id="toc-Visualization-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-In_science" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#In_science"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>In science</span> </div> </a> <ul id="toc-In_science-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-In_practical_contexts" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#In_practical_contexts"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>In practical contexts</span> </div> </a> <ul id="toc-In_practical_contexts-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Pitfalls" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Pitfalls"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Pitfalls</span> </div> </a> <ul id="toc-Pitfalls-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Computer simulation</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" 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Available in 38 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-38" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">38 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%AD%D8%A7%D9%83%D8%A7%D8%A9_%D8%A8%D8%A7%D9%84%D8%AD%D8%A7%D8%B3%D9%88%D8%A8" title="محاكاة بالحاسوب – Arabic" lang="ar" hreflang="ar" data-title="محاكاة بالحاسوب" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BC%D0%BF%D1%8E%D1%82%D1%8A%D1%80%D0%BD%D0%B0_%D1%81%D0%B8%D0%BC%D1%83%D0%BB%D0%B0%D1%86%D0%B8%D1%8F" title="Компютърна симулация – Bulgarian" lang="bg" hreflang="bg" data-title="Компютърна симулация" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Simulaci%C3%B3_d%27ordinador" title="Simulació d'ordinador – Catalan" lang="ca" hreflang="ca" data-title="Simulació d'ordinador" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Po%C4%8D%C3%ADta%C4%8Dov%C3%A1_simulace" title="Počítačová simulace – Czech" lang="cs" hreflang="cs" data-title="Počítačová simulace" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Computersimulation" title="Computersimulation – Danish" lang="da" hreflang="da" data-title="Computersimulation" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Computersimulation" title="Computersimulation – German" lang="de" hreflang="de" data-title="Computersimulation" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Arvutisimulatsioon" title="Arvutisimulatsioon – Estonian" lang="et" hreflang="et" data-title="Arvutisimulatsioon" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Simulaci%C3%B3n_(inform%C3%A1tica)" title="Simulación (informática) – Spanish" lang="es" hreflang="es" data-title="Simulación (informática)" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Komputilsimulado" title="Komputilsimulado – Esperanto" lang="eo" hreflang="eo" data-title="Komputilsimulado" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B4%D8%A8%DB%8C%D9%87%E2%80%8C%D8%B3%D8%A7%D8%B2%DB%8C_%DA%A9%D8%A7%D9%85%D9%BE%DB%8C%D9%88%D8%AA%D8%B1%DB%8C" title="شبیه‌سازی کامپیوتری – Persian" lang="fa" hreflang="fa" data-title="شبیه‌سازی کامپیوتری" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Simulation_informatique" title="Simulation informatique – French" lang="fr" hreflang="fr" data-title="Simulation informatique" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%BB%B4%ED%93%A8%ED%84%B0_%EC%8B%9C%EB%AE%AC%EB%A0%88%EC%9D%B4%EC%85%98" title="컴퓨터 시뮬레이션 – Korean" lang="ko" hreflang="ko" data-title="컴퓨터 시뮬레이션" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%85%E0%A4%AD%E0%A4%BF%E0%A4%95%E0%A4%B2%E0%A4%BF%E0%A4%A4%E0%A5%8D%E0%A4%B0_%E0%A4%85%E0%A4%A8%E0%A5%81%E0%A4%95%E0%A4%BE%E0%A4%B0" title="अभिकलित्र अनुकार – Hindi" lang="hi" hreflang="hi" data-title="अभिकलित्र अनुकार" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Komputerala_simulo" title="Komputerala simulo – Ido" lang="io" hreflang="io" data-title="Komputerala simulo" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Simulasi_komputer" title="Simulasi komputer – Indonesian" lang="id" hreflang="id" data-title="Simulasi komputer" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-zu mw-list-item"><a href="https://zu.wikipedia.org/wiki/UmFefenyeko_wesiCikizi" title="UmFefenyeko wesiCikizi – Zulu" lang="zu" hreflang="zu" data-title="UmFefenyeko wesiCikizi" data-language-autonym="IsiZulu" data-language-local-name="Zulu" class="interlanguage-link-target"><span>IsiZulu</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A1%D7%99%D7%9E%D7%95%D7%9C%D7%A6%D7%99%D7%94_%D7%9E%D7%9E%D7%95%D7%97%D7%A9%D7%91%D7%AA" title="סימולציה ממוחשבת – Hebrew" lang="he" hreflang="he" data-title="סימולציה ממוחשבת" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9C%D0%B0%D1%88%D0%B8%D0%BD%D0%B0%D0%BB%D1%8B%D2%9B_%D2%B1%D2%9B%D1%81%D0%B0%D1%82%D1%82%D1%8B%D1%80%D1%83" title="Машиналық ұқсаттыру – Kazakh" lang="kk" hreflang="kk" data-title="Машиналық ұқсаттыру" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Simulatio_computatralis" title="Simulatio computatralis – Latin" lang="la" hreflang="la" data-title="Simulatio computatralis" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Penyelakuan_komputer" title="Penyelakuan komputer – Malay" lang="ms" hreflang="ms" data-title="Penyelakuan komputer" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/Modelaige_cumputacional" title="Modelaige cumputacional – Mirandese" lang="mwl" hreflang="mwl" data-title="Modelaige cumputacional" data-language-autonym="Mirandés" data-language-local-name="Mirandese" class="interlanguage-link-target"><span>Mirandés</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BC%D0%BF%D1%8C%D1%8E%D1%82%D0%B5%D1%80%D0%B8%D0%B9%D0%BD_%D1%81%D0%B8%D0%BC%D1%83%D0%BB%D1%8F%D1%86%D0%B8" title="Компьютерийн симуляци – Mongolian" lang="mn" hreflang="mn" data-title="Компьютерийн симуляци" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Computersimulatie" title="Computersimulatie – Dutch" lang="nl" hreflang="nl" data-title="Computersimulatie" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Datasimulering" title="Datasimulering – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Datasimulering" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Symulacja_komputerowa" title="Symulacja komputerowa – Polish" lang="pl" hreflang="pl" data-title="Symulacja komputerowa" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Modelagem_computacional" title="Modelagem computacional – Portuguese" lang="pt" hreflang="pt" data-title="Modelagem computacional" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BC%D0%BF%D1%8C%D1%8E%D1%82%D0%B5%D1%80%D0%BD%D0%BE%D0%B5_%D0%BC%D0%BE%D0%B4%D0%B5%D0%BB%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D0%B5" title="Компьютерное моделирование – Russian" lang="ru" hreflang="ru" data-title="Компьютерное моделирование" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Computer_model" title="Computer model – Simple English" lang="en-simple" hreflang="en-simple" data-title="Computer model" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Po%C4%8D%C3%ADta%C4%8Dov%C3%A1_simul%C3%A1cia" title="Počítačová simulácia – Slovak" lang="sk" hreflang="sk" data-title="Počítačová simulácia" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Ra%C4%8Dunalni%C5%A1ka_simulacija" title="Računalniška simulacija – Slovenian" lang="sl" hreflang="sl" data-title="Računalniška simulacija" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A0%D0%B0%D1%87%D1%83%D0%BD%D0%B0%D1%80%D1%81%D0%BA%D0%B0_%D1%81%D0%B8%D0%BC%D1%83%D0%BB%D0%B0%D1%86%D0%B8%D1%98%D0%B0" title="Рачунарска симулација – Serbian" lang="sr" hreflang="sr" data-title="Рачунарска симулација" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Tietokonesimulointi" title="Tietokonesimulointi – Finnish" lang="fi" hreflang="fi" data-title="Tietokonesimulointi" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Bilgisayar_sim%C3%BClasyonu" title="Bilgisayar simülasyonu – Turkish" lang="tr" hreflang="tr" data-title="Bilgisayar simülasyonu" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A7%D0%B8%D1%81%D0%B5%D0%BB%D1%8C%D0%BD%D0%B5_%D0%BC%D0%BE%D0%B4%D0%B5%D0%BB%D1%8E%D0%B2%D0%B0%D0%BD%D0%BD%D1%8F" title="Чисельне моделювання – Ukrainian" lang="uk" hreflang="uk" data-title="Чисельне моделювання" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/M%C3%B4_ph%E1%BB%8Fng_m%C3%A1y_t%C3%ADnh" title="Mô phỏng máy tính – Vietnamese" lang="vi" hreflang="vi" data-title="Mô phỏng máy tính" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E8%AE%A1%E7%AE%97%E6%9C%BA%E4%BB%BF%E7%9C%9F" title="计算机仿真 – Wu" lang="wuu" hreflang="wuu" data-title="计算机仿真" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%9B%BB%E8%85%A6%E6%A8%A1%E6%93%AC" title="電腦模擬 – Cantonese" lang="yue" hreflang="yue" data-title="電腦模擬" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E8%AE%A1%E7%AE%97%E6%9C%BA%E6%A8%A1%E6%8B%9F" title="计算机模拟 – Chinese" lang="zh" hreflang="zh" data-title="计算机模拟" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div 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id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"><span class="mw-redirectedfrom">(Redirected from <a href="/w/index.php?title=Computer_model&redirect=no" class="mw-redirect" title="Computer model">Computer model</a>)</span></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Process of mathematical modelling, performed on a computer</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">This article is about computer model within a scientific context. For simulating a computer on a computer, see <a href="/wiki/Emulator" title="Emulator">emulator</a>.</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">"Computer model" redirects here. For computer models of 3 dimensional objects, see <a href="/wiki/3D_modeling" title="3D modeling">3D modeling</a>.</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">"Digital model" redirects here. For digital twinning, see <a href="/wiki/Digital_twin" title="Digital twin">Digital twin</a>. For virtual fictional characters, see <a href="/wiki/Virtual_influencer" title="Virtual influencer">Virtual influencer</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-More_citations_needed plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article <b>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Computer_simulation" title="Special:EditPage/Computer simulation">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and removed.<br /><small><span class="plainlinks"><i>Find sources:</i> <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&q=%22Computer+simulation%22">"Computer simulation"</a> – <a rel="nofollow" class="external text" href="https://www.google.com/search?tbm=nws&q=%22Computer+simulation%22+-wikipedia&tbs=ar:1">news</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22Computer+simulation%22&tbs=bkt:s&tbm=bks">newspapers</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?tbs=bks:1&q=%22Computer+simulation%22+-wikipedia">books</a> <b>·</b> <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22Computer+simulation%22">scholar</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22Computer+simulation%22&acc=on&wc=on">JSTOR</a></span></small></span> <span class="date-container"><i>(<span class="date">December 2022</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Typhoon_Mawar_2005_computer_simulation_thumbnail.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Typhoon_Mawar_2005_computer_simulation_thumbnail.gif/300px-Typhoon_Mawar_2005_computer_simulation_thumbnail.gif" decoding="async" width="300" height="269" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/8/8b/Typhoon_Mawar_2005_computer_simulation_thumbnail.gif 1.5x" data-file-width="450" data-file-height="403" /></a><figcaption>A 48-hour computer simulation of <a href="/wiki/2005_Pacific_typhoon_season#Typhoon_Mawar" title="2005 Pacific typhoon season">Typhoon Mawar</a> using the <a href="/wiki/Weather_Research_and_Forecasting_model" class="mw-redirect" title="Weather Research and Forecasting model">Weather Research and Forecasting model</a> </figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Molecular_simulation_process.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Molecular_simulation_process.svg/400px-Molecular_simulation_process.svg.png" decoding="async" width="400" height="327" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Molecular_simulation_process.svg/600px-Molecular_simulation_process.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Molecular_simulation_process.svg/800px-Molecular_simulation_process.svg.png 2x" data-file-width="780" data-file-height="638" /></a><figcaption>Process of building a computer model, and the interplay between experiment, simulation, and theory</figcaption></figure> <p><b>Computer simulation</b> is the running of a <a href="/wiki/Mathematical_modelling" class="mw-redirect" title="Mathematical modelling">mathematical model</a> on a <a href="/wiki/Computer" title="Computer">computer</a>, the <a href="/wiki/Model" title="Model">model</a> being designed to represent the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be determined by comparing their results to the real-world outcomes they aim to predict. Computer <a href="/wiki/Simulation" title="Simulation">simulations</a> have become a useful tool for the mathematical modeling of many natural systems in <a href="/wiki/Physics" title="Physics">physics</a> (<a href="/wiki/Computational_physics" title="Computational physics">computational physics</a>), <a href="/wiki/Astrophysics" title="Astrophysics">astrophysics</a>, <a href="/wiki/Climatology" title="Climatology">climatology</a>, <a href="/wiki/Chemistry" title="Chemistry">chemistry</a>, <a href="/wiki/Biology" title="Biology">biology</a> and <a href="/wiki/Manufacturing" title="Manufacturing">manufacturing</a>, as well as human systems in <a href="/wiki/Economics" title="Economics">economics</a>, <a href="/wiki/Psychology" title="Psychology">psychology</a>, <a href="/wiki/Social_science" title="Social science">social science</a>, <a href="/wiki/Health_care" title="Health care">health care</a> and <a href="/wiki/Engineering" title="Engineering">engineering</a>. Simulation of a system is represented as the running of the system's model. It can be used to explore and gain new insights into new <a href="/wiki/Technology" title="Technology">technology</a> and to estimate the performance of systems too complex for <a href="/wiki/Analytical_solution" class="mw-redirect" title="Analytical solution">analytical solutions</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>Computer simulations are realized by running <a href="/wiki/Computer_program" title="Computer program">computer programs</a> that can be either small, running almost instantly on small devices, or large-scale programs that run for hours or days on network-based groups of computers. The scale of events being simulated by computer simulations has far exceeded anything possible (or perhaps even imaginable) using traditional paper-and-pencil mathematical modeling. In 1997, a desert-battle simulation of one force invading another involved the modeling of 66,239 tanks, trucks and other vehicles on simulated terrain around <a href="/wiki/Kuwait" title="Kuwait">Kuwait</a>, using multiple supercomputers in the <a href="/wiki/DoD" class="mw-redirect" title="DoD">DoD</a> High Performance Computer Modernization Program.<sup id="cite_ref-JPLsim_2-0" class="reference"><a href="#cite_note-JPLsim-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Other examples include a 1-billion-atom model of material deformation;<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> a 2.64-million-atom model of the complex protein-producing organelle of all living organisms, the <a href="/wiki/Ribosome" title="Ribosome">ribosome</a>, in 2005;<sup id="cite_ref-LANLsim_4-0" class="reference"><a href="#cite_note-LANLsim-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> a complete simulation of the life cycle of <i><a href="/wiki/Mycoplasma_genitalium" title="Mycoplasma genitalium">Mycoplasma genitalium</a></i> in 2012; and the <a href="/wiki/Blue_Brain" class="mw-redirect" title="Blue Brain">Blue Brain</a> project at <a href="/wiki/EPFL" class="mw-redirect" title="EPFL">EPFL</a> (Switzerland), begun in May 2005 to create the first computer simulation of the entire human brain, right down to the molecular level.<sup id="cite_ref-Brainsim_5-0" class="reference"><a href="#cite_note-Brainsim-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>Because of the computational cost of simulation, <a href="/wiki/Computer_experiment" title="Computer experiment">computer experiments</a> are used to perform inference such as <a href="/wiki/Uncertainty_quantification" title="Uncertainty quantification">uncertainty quantification</a>.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Simulation_versus_model">Simulation versus model</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computer_simulation&action=edit&section=1" title="Edit section: Simulation versus model"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A model consists of the equations used to capture the behavior of a system. By contrast, computer simulation is the actual running of the program that perform algorithms which solve those equations, often in an approximate manner. Simulation, therefore, is the process of running a model. Thus one would not "build a simulation"; instead, one would "build a model (or a simulator)", and then either "run the model" or equivalently "run a simulation". </p> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computer_simulation&action=edit&section=2" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Computer simulation developed hand-in-hand with the rapid growth of the computer, following its first large-scale deployment during the <a href="/wiki/Manhattan_Project" title="Manhattan Project">Manhattan Project</a> in <a href="/wiki/World_War_II" title="World War II">World War II</a> to model the process of <a href="/wiki/Nuclear_weapon" title="Nuclear weapon">nuclear detonation</a>. It was a simulation of 12 <a href="/wiki/Hard_spheres" title="Hard spheres">hard spheres</a> using a <a href="/wiki/Monte_Carlo_method" title="Monte Carlo method">Monte Carlo algorithm</a>. Computer simulation is often used as an adjunct to, or substitute for, modeling systems for which simple <a href="/wiki/Closed-form_solution" class="mw-redirect" title="Closed-form solution">closed form analytic solutions</a> are not possible. There are many types of computer simulations; their common feature is the attempt to generate a sample of representative scenarios for a model in which a complete enumeration of all possible states of the model would be prohibitive or impossible.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Data_preparation">Data preparation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computer_simulation&action=edit&section=3" title="Edit section: Data preparation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The external data requirements of simulations and models vary widely. For some, the input might be just a few numbers (for example, simulation of a waveform of AC electricity on a wire), while others might require terabytes of information (such as weather and climate models). </p><p>Input sources also vary widely: </p> <ul><li>Sensors and other physical devices connected to the model;</li> <li>Control surfaces used to direct the progress of the simulation in some way;</li> <li>Current or historical data entered by hand;</li> <li>Values extracted as a by-product from other processes;</li> <li>Values output for the purpose by other simulations, models, or processes.</li></ul> <p>Lastly, the time at which data is available varies: </p> <ul><li>"invariant" data is often built into the model code, either because the value is truly invariant (e.g., the value of π) or because the designers consider the value to be invariant for all cases of interest;</li> <li>data can be entered into the simulation when it starts up, for example by reading one or more files, or by reading data from a <a href="/wiki/Preprocessor_(CAE)" title="Preprocessor (CAE)">preprocessor</a>;</li> <li>data can be provided during the simulation run, for example by a sensor network.</li></ul> <p>Because of this variety, and because diverse simulation systems have many common elements, there are a large number of specialized <a href="/wiki/Simulation_language" title="Simulation language">simulation languages</a>. The best-known may be <a href="/wiki/Simula" title="Simula">Simula</a>. There are now many others. </p><p>Systems that accept data from external sources must be very careful in knowing what they are receiving. While it is easy for computers to read in values from text or binary files, what is much harder is knowing what the <a href="/wiki/Accuracy" class="mw-redirect" title="Accuracy">accuracy</a> (compared to <a href="/wiki/Graphic_display_resolutions" class="mw-redirect" title="Graphic display resolutions">measurement resolution</a> and <a href="/wiki/Accuracy_and_precision" title="Accuracy and precision">precision</a>) of the values are. Often they are expressed as "error bars", a minimum and maximum deviation from the value range within which the true value (is expected to) lie. Because digital computer mathematics is not perfect, rounding and truncation errors multiply this error, so it is useful to perform an "error analysis"<sup id="cite_ref-Taylor_8-0" class="reference"><a href="#cite_note-Taylor-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> to confirm that values output by the simulation will still be usefully accurate. </p> <div class="mw-heading mw-heading2"><h2 id="Types">Types</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computer_simulation&action=edit&section=4" title="Edit section: Types"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Models used for computer simulations can be classified according to several independent pairs of attributes, including: </p> <ul><li><a href="/wiki/Stochastic_process" title="Stochastic process">Stochastic</a> or <a href="/wiki/Deterministic_algorithm" title="Deterministic algorithm">deterministic</a> (and as a special case of deterministic, chaotic) – see external links below for examples of stochastic vs. deterministic simulations</li> <li>Steady-state or dynamic</li> <li><a href="/wiki/Continuous_function" title="Continuous function">Continuous</a> or <a href="/wiki/Discrete_mathematics" title="Discrete mathematics">discrete</a> (and as an important special case of discrete, <a href="/wiki/Discrete_event_simulation" class="mw-redirect" title="Discrete event simulation">discrete event</a> or DE models)</li> <li><a href="/wiki/Dynamic_simulation" title="Dynamic simulation">Dynamic system simulation</a>, e.g. electric systems, hydraulic systems or multi-body mechanical systems (described primarily by DAE:s) or dynamics simulation of field problems, e.g. CFD of FEM simulations (described by PDE:s).</li> <li>Local or <a href="/wiki/Distributed_computing" title="Distributed computing">distributed</a>.</li></ul> <p>Another way of categorizing models is to look at the underlying data structures. For time-stepped simulations, there are two main classes: </p> <ul><li>Simulations which store their data in regular grids and require only next-neighbor access are called <a href="/wiki/Stencil_code" class="mw-redirect" title="Stencil code">stencil codes</a>. Many <a href="/wiki/Computational_fluid_dynamics" title="Computational fluid dynamics">CFD</a> applications belong to this category.</li> <li>If the underlying graph is not a regular grid, the model may belong to the <a href="/wiki/Meshfree_method" class="mw-redirect" title="Meshfree method">meshfree method</a> class.</li></ul> <p>For steady-state simulations, equations define the relationships between elements of the modeled system and attempt to find a state in which the system is in equilibrium. Such models are often used in simulating physical systems, as a simpler modeling case before dynamic simulation is attempted. </p> <ul><li>Dynamic simulations attempt to capture changes in a system in response to (usually changing) input signals.</li> <li><i><a href="/wiki/Stochastic_process" title="Stochastic process">Stochastic</a></i> models use <i><a href="/wiki/Random_number_generator" class="mw-redirect" title="Random number generator">random number generators</a></i> to model chance or random events;</li> <li>A <i><a href="/wiki/Discrete_event_simulation" class="mw-redirect" title="Discrete event simulation">discrete event simulation</a></i> (DES) manages events in time. Most computer, logic-test and fault-tree simulations are of this type. In this type of simulation, the simulator maintains a queue of events sorted by the simulated time they should occur. The simulator reads the queue and triggers new events as each event is processed. It is not important to execute the simulation in real time. It is often more important to be able to access the data produced by the simulation and to discover logic defects in the design or the sequence of events.</li> <li>A <i>continuous dynamic simulation</i> performs numerical solution of <a href="/wiki/Differential_algebraic_equation" class="mw-redirect" title="Differential algebraic equation">differential-algebraic equations</a> or <a href="/wiki/Differential_equations" class="mw-redirect" title="Differential equations">differential equations</a> (either <a href="/wiki/Partial_differential_equation" title="Partial differential equation">partial</a> or <a href="/wiki/Ordinary_differential_equation" title="Ordinary differential equation">ordinary</a>). Periodically, the simulation program solves all the equations and uses the numbers to change the state and output of the simulation. Applications include flight simulators, <a href="/wiki/Construction_and_management_simulation_games" class="mw-redirect" title="Construction and management simulation games">construction and management simulation games</a>, <a href="/wiki/Chemical_process_modeling" title="Chemical process modeling">chemical process modeling</a>, and simulations of <a href="/wiki/Electrical_circuit" class="mw-redirect" title="Electrical circuit">electrical circuits</a>. Originally, these kinds of simulations were actually implemented on <a href="/wiki/Analog_computer" title="Analog computer">analog computers</a>, where the differential equations could be represented directly by various electrical components such as <a href="/wiki/Op-amp" class="mw-redirect" title="Op-amp">op-amps</a>. By the late 1980s, however, most "analog" simulations were run on conventional <a href="/wiki/Digital_computer" class="mw-redirect" title="Digital computer">digital computers</a> that <a href="/wiki/Emulator" title="Emulator">emulate</a> the behavior of an analog computer.</li> <li>A special type of discrete simulation that does not rely on a model with an underlying equation, but can nonetheless be represented formally, is <a href="/wiki/Agent-based_model" title="Agent-based model">agent-based simulation</a>. In agent-based simulation, the individual entities (such as molecules, cells, trees or consumers) in the model are represented directly (rather than by their density or concentration) and possess an internal state and set of behaviors or rules that determine how the agent's state is updated from one time-step to the next.</li> <li><a href="/wiki/Distributed_computing" title="Distributed computing">Distributed</a> models run on a network of interconnected computers, possibly through the <a href="/wiki/Internet" title="Internet">Internet</a>. Simulations dispersed across multiple host computers like this are often referred to as "distributed simulations". There are several standards for distributed simulation, including <a href="/wiki/Aggregate_Level_Simulation_Protocol" title="Aggregate Level Simulation Protocol">Aggregate Level Simulation Protocol</a> (ALSP), <a href="/wiki/Distributed_Interactive_Simulation" title="Distributed Interactive Simulation">Distributed Interactive Simulation</a> (DIS), the <a href="/wiki/High_Level_Architecture_(simulation)" class="mw-redirect" title="High Level Architecture (simulation)">High Level Architecture (simulation)</a> (HLA) and the <a href="/wiki/Test_and_Training_Enabling_Architecture" title="Test and Training Enabling Architecture">Test and Training Enabling Architecture</a> (TENA).</li></ul> <div class="mw-heading mw-heading2"><h2 id="Visualization">Visualization</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computer_simulation&action=edit&section=5" title="Edit section: Visualization"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Formerly, the output data from a computer simulation was sometimes presented in a table or a matrix showing how data were affected by numerous changes in the simulation <a href="/wiki/Parameter_(computer_programming)" title="Parameter (computer programming)">parameters</a>. The use of the matrix format was related to traditional use of the matrix concept in <a href="/wiki/Mathematical_model" title="Mathematical model">mathematical models</a>. However, psychologists and others noted that humans could quickly perceive trends by looking at graphs or even moving-images or motion-pictures generated from the data, as displayed by <a href="/wiki/Computer-generated-imagery" class="mw-redirect" title="Computer-generated-imagery">computer-generated-imagery</a> (CGI) animation. Although observers could not necessarily read out numbers or quote math formulas, from observing a moving weather chart they might be able to predict events (and "see that rain was headed their way") much faster than by scanning tables of rain-cloud <a href="/wiki/Coordinate" class="mw-redirect" title="Coordinate">coordinates</a>. Such intense graphical displays, which transcended the world of numbers and formulae, sometimes also led to output that lacked a coordinate grid or omitted timestamps, as if straying too far from numeric data displays. Today, <a href="/wiki/Weather_forecasting" title="Weather forecasting">weather forecasting</a> models tend to balance the view of moving rain/snow clouds against a map that uses numeric coordinates and numeric timestamps of events. </p><p>Similarly, CGI computer simulations of <a href="/wiki/CAT_scan" class="mw-redirect" title="CAT scan">CAT scans</a> can simulate how a <a href="/wiki/Brain_cancer" class="mw-redirect" title="Brain cancer">tumor</a> might shrink or change during an extended period of medical treatment, presenting the passage of time as a spinning view of the visible human head, as the tumor changes. </p><p>Other applications of CGI computer simulations are being developed<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Manual_of_Style/Dates_and_numbers#Chronological_items" title="Wikipedia:Manual of Style/Dates and numbers"><span title="The time period mentioned near this tag is ambiguous. (December 2022)">as of?</span></a></i>]</sup> to graphically display large amounts of data, in motion, as changes occur during a simulation run. </p> <div class="mw-heading mw-heading2"><h2 id="In_science">In science</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computer_simulation&action=edit&section=6" title="Edit section: In science"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Osmosis_computer_simulation.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/45/Osmosis_computer_simulation.jpg/250px-Osmosis_computer_simulation.jpg" decoding="async" width="250" height="222" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/45/Osmosis_computer_simulation.jpg/375px-Osmosis_computer_simulation.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/45/Osmosis_computer_simulation.jpg/500px-Osmosis_computer_simulation.jpg 2x" data-file-width="922" data-file-height="820" /></a><figcaption>Computer simulation of the process of <a href="/wiki/Osmosis" title="Osmosis">osmosis</a> </figcaption></figure> <p>Generic examples of types of computer simulations in science, which are derived from an underlying mathematical description: </p> <ul><li>a numerical simulation of <a href="/wiki/Differential_equation" title="Differential equation">differential equations</a> that cannot be solved analytically, theories that involve continuous systems such as phenomena in <a href="/wiki/Physical_cosmology" title="Physical cosmology">physical cosmology</a>, <a href="/wiki/Fluid_dynamics" title="Fluid dynamics">fluid dynamics</a> (e.g., <a href="/wiki/Climate_model" title="Climate model">climate models</a>, <a href="/wiki/Roadway_noise" title="Roadway noise">roadway noise</a> models, <a href="/wiki/Roadway_air_dispersion_model" class="mw-redirect" title="Roadway air dispersion model">roadway air dispersion models</a>), <a href="/wiki/Continuum_mechanics" title="Continuum mechanics">continuum mechanics</a> and <a href="/wiki/Chemical_kinetics" title="Chemical kinetics">chemical kinetics</a> fall into this category.</li> <li>a <a href="/wiki/Stochastic" title="Stochastic">stochastic</a> simulation, typically used for discrete systems where events occur <a href="/wiki/Probabilistic" class="mw-redirect" title="Probabilistic">probabilistically</a> and which cannot be described directly with differential equations (this is a <i>discrete</i> simulation in the above sense). Phenomena in this category include <a href="/wiki/Genetic_drift" title="Genetic drift">genetic drift</a>, <a href="/wiki/Biochemical" class="mw-redirect" title="Biochemical">biochemical</a><sup id="cite_ref-:0_9-0" class="reference"><a href="#cite_note-:0-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> or <a href="/wiki/Gene_regulatory_network" title="Gene regulatory network">gene regulatory networks</a> with small numbers of molecules. (see also: <a href="/wiki/Monte_Carlo_method" title="Monte Carlo method">Monte Carlo method</a>).</li> <li>multiparticle simulation of the response of nanomaterials at multiple scales to an applied force for the purpose of modeling their thermoelastic and thermodynamic properties. Techniques used for such simulations are <a href="/wiki/Molecular_dynamics" title="Molecular dynamics">Molecular dynamics</a>, <a href="/wiki/Molecular_mechanics" title="Molecular mechanics">Molecular mechanics</a>, <a href="/wiki/Monte_Carlo_method" title="Monte Carlo method">Monte Carlo method</a>, and <a href="/wiki/Multiscale_Green%27s_function" title="Multiscale Green's function">Multiscale Green's function</a>.</li></ul> <p>Specific examples of computer simulations include: </p> <ul><li>statistical simulations based upon an agglomeration of a large number of input profiles, such as the forecasting of equilibrium <a href="/wiki/Temperature" title="Temperature">temperature</a> of receiving waters, allowing the gamut of <a href="/wiki/Meteorological" class="mw-redirect" title="Meteorological">meteorological</a> data to be input for a specific locale. This technique was developed for <a href="/wiki/Thermal_pollution" title="Thermal pollution">thermal pollution</a> forecasting.</li> <li>agent based simulation has been used effectively in <a href="/wiki/Ecology" title="Ecology">ecology</a>, where it is often called "individual based modeling" and is used in situations for which individual variability in the agents cannot be neglected, such as <a href="/wiki/Population_dynamics" title="Population dynamics">population dynamics</a> of <a href="/wiki/Salmon" title="Salmon">salmon</a> and <a href="/wiki/Trout" title="Trout">trout</a> (most purely mathematical models assume all trout behave identically).</li> <li>time stepped dynamic model. In hydrology there are several such <a href="/wiki/Hydrology_transport_model" class="mw-redirect" title="Hydrology transport model">hydrology transport models</a> such as the <a href="/wiki/SWMM" class="mw-redirect" title="SWMM">SWMM</a> and <a href="/wiki/DSSAM_Model" title="DSSAM Model">DSSAM Models</a> developed by the <a href="/wiki/U.S._Environmental_Protection_Agency" class="mw-redirect" title="U.S. Environmental Protection Agency">U.S. Environmental Protection Agency</a> for river water quality forecasting.</li> <li>computer simulations have also been used to formally <a href="/wiki/Computational_cognition" title="Computational cognition">model theories of human cognition</a> and performance, e.g., <a href="/wiki/ACT-R" title="ACT-R">ACT-R</a>.</li> <li>computer simulation using <a href="/wiki/Molecular_modeling" class="mw-redirect" title="Molecular modeling">molecular modeling</a> for <a href="/wiki/Drug_discovery" title="Drug discovery">drug discovery</a>.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup></li> <li>computer simulation to model viral infection in mammalian cells.<sup id="cite_ref-:0_9-1" class="reference"><a href="#cite_note-:0-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup></li> <li>computer simulation for studying the selective sensitivity of bonds by mechanochemistry during grinding of organic molecules.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Computational_fluid_dynamics" title="Computational fluid dynamics">Computational fluid dynamics</a> simulations are used to simulate the behaviour of flowing air, water and other fluids. One-, two- and three-dimensional models are used. A one-dimensional model might simulate the effects of <a href="/wiki/Water_hammer" title="Water hammer">water hammer</a> in a pipe. A two-dimensional model might be used to simulate the drag forces on the cross-section of an aeroplane wing. A three-dimensional simulation might estimate the heating and cooling requirements of a large building.</li> <li>An understanding of statistical thermodynamic molecular theory is fundamental to the appreciation of molecular solutions. Development of the Potential Distribution Theorem (PDT) allows this complex subject to be simplified to down-to-earth presentations of molecular theory.</li></ul> <p>Notable, and sometimes controversial, computer simulations used in science include: <a href="/wiki/Donella_Meadows" title="Donella Meadows">Donella Meadows</a>' <a href="/wiki/World3" title="World3">World3</a> used in the <i><a href="/wiki/Limits_to_Growth" class="mw-redirect" title="Limits to Growth">Limits to Growth</a></i>, <a href="/wiki/James_Lovelock" title="James Lovelock">James Lovelock's</a> <a href="/wiki/Daisyworld" title="Daisyworld">Daisyworld</a> and Thomas Ray's <a href="/wiki/Tierra_(computer_simulation)" title="Tierra (computer simulation)">Tierra</a>. </p><p>In social sciences, computer simulation is an integral component of the five angles of analysis fostered by the data percolation methodology,<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> which also includes qualitative and quantitative methods, reviews of the literature (including scholarly), and interviews with experts, and which forms an extension of data triangulation. Of course, similar to any other scientific method, <a href="/wiki/Replication_(scientific_method)" class="mw-redirect" title="Replication (scientific method)">replication</a> is an important part of computational modeling <sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="In_practical_contexts">In practical contexts</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computer_simulation&action=edit&section=7" title="Edit section: In practical contexts"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-More_citations_needed_section plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Computer_simulation" title="Special:EditPage/Computer simulation">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a> in this section. Unsourced material may be challenged and removed.</span> <span class="date-container"><i>(<span class="date">June 2022</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>Computer simulations are used in a wide variety of practical contexts, such as: </p> <ul><li>analysis of <a href="/wiki/Air_pollutant" class="mw-redirect" title="Air pollutant">air pollutant</a> dispersion using <a href="/wiki/Atmospheric_dispersion_modeling" title="Atmospheric dispersion modeling">atmospheric dispersion modeling</a></li> <li>As a possible humane alternative to live <a href="/wiki/Animal_testing" title="Animal testing">animal testing</a> in respect to <a href="/wiki/Animal_rights" title="Animal rights">animal rights</a>.</li> <li>design of complex systems such as <a href="/wiki/Aircraft" title="Aircraft">aircraft</a> and also <a href="/wiki/Logistics" title="Logistics">logistics</a> systems.</li> <li>design of <a href="/wiki/Noise_barrier" title="Noise barrier">noise barriers</a> to effect roadway <a href="/wiki/Noise_mitigation" class="mw-redirect" title="Noise mitigation">noise mitigation</a></li> <li>modeling of <a href="/wiki/Application_performance_management" title="Application performance management">application performance</a><sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Flight_simulator" title="Flight simulator">flight simulators</a> to train pilots</li> <li><a href="/wiki/Atmospheric_model" title="Atmospheric model">weather forecasting</a></li> <li><a href="/wiki/Risk_management" title="Risk management">forecasting of risk</a></li> <li>simulation of electrical circuits</li> <li><a href="/wiki/Power_system_simulation" title="Power system simulation">Power system simulation</a></li> <li>simulation of other computers is <a href="/wiki/Emulator" title="Emulator">emulation</a>.</li> <li>forecasting of prices on financial markets (for example <a href="/wiki/Adaptive_Modeler" title="Adaptive Modeler">Adaptive Modeler</a>)</li> <li>behavior of structures (such as buildings and industrial parts) under stress and other conditions</li> <li>design of industrial processes, such as chemical processing plants</li> <li><a href="/wiki/Strategic_management" title="Strategic management">strategic management</a> and <a href="/wiki/Organizational_studies" class="mw-redirect" title="Organizational studies">organizational studies</a></li> <li><a href="/wiki/Reservoir_simulation" title="Reservoir simulation">reservoir simulation</a> for the petroleum engineering to model the subsurface reservoir</li> <li>process engineering simulation tools.</li> <li><a href="/wiki/Robotics_suite" title="Robotics suite">robot simulators</a> for the design of robots and robot control algorithms</li> <li><a href="/wiki/UrbanSim" title="UrbanSim">urban simulation models</a> that simulate dynamic patterns of urban development and responses to urban land use and transportation policies.</li> <li><a href="/wiki/Traffic_engineering_(transportation)" title="Traffic engineering (transportation)">traffic engineering</a> to plan or redesign parts of the street network from single junctions over cities to a national highway network to transportation system planning, design and operations. See a more detailed article on <a href="/wiki/Traffic_Simulation" class="mw-redirect" title="Traffic Simulation">Simulation in Transportation</a>.</li> <li>modeling car crashes to test safety mechanisms in new vehicle models.</li> <li><a href="/wiki/Theoretical_production_ecology" title="Theoretical production ecology">crop-soil systems</a> in agriculture, via dedicated software frameworks (e.g. <a href="/wiki/BioMA" title="BioMA">BioMA</a>, OMS3, APSIM)</li></ul> <p>The reliability and the trust people put in computer simulations depends on the <a href="/wiki/Validity_(logic)" title="Validity (logic)">validity</a> of the simulation <a href="/wiki/Model_(abstract)" class="mw-redirect" title="Model (abstract)">model</a>, therefore <a href="/wiki/Verification_and_validation" title="Verification and validation">verification and validation</a> are of crucial importance in the development of computer simulations. Another important aspect of computer simulations is that of reproducibility of the results, meaning that a simulation model should not provide a different answer for each execution. Although this might seem obvious, this is a special point of attention<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:EDITORIALIZING" class="mw-redirect" title="Wikipedia:EDITORIALIZING"><span title="A statement that draws an independent conclusion. (December 2022)">editorializing</span></a></i>]</sup> in <a href="/wiki/Stochastic_simulation" title="Stochastic simulation">stochastic simulations</a>, where random numbers should actually be semi-random numbers. An exception to reproducibility are human-in-the-loop simulations such as flight simulations and <a href="/wiki/Computer_games" class="mw-redirect" title="Computer games">computer games</a>. Here a human is part of the simulation and thus influences the outcome in a way that is hard, if not impossible, to reproduce exactly. </p><p><a href="/wiki/Vehicle" title="Vehicle">Vehicle</a> manufacturers make use of computer simulation to test safety features in new designs. By building a copy of the car in a physics simulation environment, they can save the hundreds of thousands of dollars that would otherwise be required to build and test a unique prototype. Engineers can step through the simulation milliseconds at a time to determine the exact stresses being put upon each section of the prototype.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Computer_graphics" title="Computer graphics">Computer graphics</a> can be used to display the results of a computer simulation. <a href="/wiki/Animations" class="mw-redirect" title="Animations">Animations</a> can be used to experience a simulation in real-time, e.g., in <a href="/wiki/Training_Simulation" class="mw-redirect" title="Training Simulation">training simulations</a>. In some cases animations may also be useful in faster than real-time or even slower than real-time modes. For example, faster than real-time animations can be useful in visualizing the buildup of queues in the simulation of humans evacuating a building. Furthermore, simulation results are often aggregated into static images using various ways of <a href="/wiki/Scientific_visualization" title="Scientific visualization">scientific visualization</a>. </p><p>In debugging, simulating a program execution under test (rather than executing natively) can detect far more errors than the hardware itself can detect and, at the same time, log useful debugging information such as instruction trace, memory alterations and instruction counts. This technique can also detect <a href="/wiki/Buffer_overflow" title="Buffer overflow">buffer overflow</a> and similar "hard to detect" errors as well as produce performance information and <a href="/wiki/Performance_tuning" title="Performance tuning">tuning</a> data. </p> <div class="mw-heading mw-heading2"><h2 id="Pitfalls">Pitfalls</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computer_simulation&action=edit&section=8" title="Edit section: Pitfalls"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Although sometimes ignored in computer simulations, it is very important<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:EDITORIALIZING" class="mw-redirect" title="Wikipedia:EDITORIALIZING"><span title="A statement that draws an independent conclusion. (December 2022)">editorializing</span></a></i>]</sup> to perform a <a href="/wiki/Sensitivity_analysis" title="Sensitivity analysis">sensitivity analysis</a> to ensure that the accuracy of the results is properly understood. For example, the probabilistic risk analysis of factors determining the success of an oilfield exploration program involves combining samples from a variety of statistical distributions using the <a href="/wiki/Monte_Carlo_method" title="Monte Carlo method">Monte Carlo method</a>. If, for instance, one of the key parameters (e.g., the net ratio of oil-bearing strata) is known to only one significant figure, then the result of the simulation might not be more precise than one significant figure, although it might (misleadingly) be presented as having four significant figures. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computer_simulation&action=edit&section=9" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 30em;"> <ul><li><a href="/wiki/Computational_model" title="Computational model">Computational model</a></li> <li><a href="/wiki/Digital_twin" title="Digital twin">Digital twin</a></li> <li><a href="/wiki/Illustris_project" title="Illustris project">Illustris project</a></li> <li><a href="/wiki/List_of_computer_simulation_software" title="List of computer simulation software">List of computer simulation software</a></li> <li><a href="/wiki/Scene_generator" title="Scene generator">Scene generator</a></li> <li><a href="/wiki/Simulation" title="Simulation">Simulation</a></li> <li><a href="/wiki/Simulation_hypothesis" title="Simulation hypothesis">Simulation hypothesis</a></li> <li><a href="/wiki/Simulation_software" title="Simulation software">Simulation software</a></li> <li><a href="/wiki/Simulation_video_game" title="Simulation video game">Simulation video game</a></li> <li><a href="/wiki/UniverseMachine" title="UniverseMachine">UniverseMachine</a></li> <li><a href="/wiki/Virtual_prototyping" title="Virtual prototyping">Virtual prototyping</a></li> <li><a href="/wiki/Virtual_reality" title="Virtual reality">Virtual reality</a></li> <li><a href="/wiki/Web-based_simulation" title="Web-based simulation">Web-based simulation</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computer_simulation&action=edit&section=10" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFStrogatz2007" class="citation book cs1">Strogatz, Steven (2007). "The End of Insight". In Brockman, John (ed.). <i>What is your dangerous idea?</i>. 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University Science Books. pp. 128–129. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-935702-75-0" title="Special:BookSources/978-0-935702-75-0"><bdi>978-0-935702-75-0</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150316103343/http://books.google.com/books?id=giFQcZub80oC&pg=PA128">Archived</a> from the original on 2015-03-16.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=An+Introduction+to+Error+Analysis%3A+The+Study+of+Uncertainties+in+Physical+Measurements&rft.pages=128-129&rft.pub=University+Science+Books&rft.date=1999&rft.isbn=978-0-935702-75-0&rft.au=John+Robert+Taylor&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DgiFQcZub80oC%26pg%3DPA128&rfr_id=info%3Asid%2Fen.wikipedia.org%3AComputer+simulation" class="Z3988"></span></span> </li> <li id="cite_note-:0-9"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_9-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_9-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGuptaRawlings2014" class="citation journal cs1">Gupta, Ankur; Rawlings, James B. (April 2014). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4946376">"Comparison of Parameter Estimation Methods in Stochastic Chemical Kinetic Models: Examples in Systems Biology"</a>. <i>AIChE Journal</i>. <b>60</b> (4): 1253–1268. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2014AIChE..60.1253G">2014AIChE..60.1253G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Faic.14409">10.1002/aic.14409</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0001-1541">0001-1541</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4946376">4946376</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/27429455">27429455</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=AIChE+Journal&rft.atitle=Comparison+of+Parameter+Estimation+Methods+in+Stochastic+Chemical+Kinetic+Models%3A+Examples+in+Systems+Biology&rft.volume=60&rft.issue=4&rft.pages=1253-1268&rft.date=2014-04&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC4946376%23id-name%3DPMC&rft_id=info%3Abibcode%2F2014AIChE..60.1253G&rft_id=info%3Apmid%2F27429455&rft_id=info%3Adoi%2F10.1002%2Faic.14409&rft.issn=0001-1541&rft.aulast=Gupta&rft.aufirst=Ankur&rft.au=Rawlings%2C+James+B.&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC4946376&rfr_id=info%3Asid%2Fen.wikipedia.org%3AComputer+simulation" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtanasovWaltenbergerPferschy-WenzigLinder2015" class="citation journal cs1">Atanasov, AG; Waltenberger, B; Pferschy-Wenzig, EM; Linder, T; Wawrosch, C; Uhrin, P; Temml, V; Wang, L; Schwaiger, S; Heiss, EH; Rollinger, JM; Schuster, D; Breuss, JM; Bochkov, V; Mihovilovic, MD; Kopp, B; Bauer, R; Dirsch, VM; Stuppner, H (2015). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4748402">"Discovery and resupply of pharmacologically active plant-derived natural products: A review"</a>. <i>Biotechnol Adv</i>. <b>33</b> (8): 1582–614. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.biotechadv.2015.08.001">10.1016/j.biotechadv.2015.08.001</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4748402">4748402</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/26281720">26281720</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Biotechnol+Adv&rft.atitle=Discovery+and+resupply+of+pharmacologically+active+plant-derived+natural+products%3A+A+review&rft.volume=33&rft.issue=8&rft.pages=1582-614&rft.date=2015&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC4748402%23id-name%3DPMC&rft_id=info%3Apmid%2F26281720&rft_id=info%3Adoi%2F10.1016%2Fj.biotechadv.2015.08.001&rft.aulast=Atanasov&rft.aufirst=AG&rft.au=Waltenberger%2C+B&rft.au=Pferschy-Wenzig%2C+EM&rft.au=Linder%2C+T&rft.au=Wawrosch%2C+C&rft.au=Uhrin%2C+P&rft.au=Temml%2C+V&rft.au=Wang%2C+L&rft.au=Schwaiger%2C+S&rft.au=Heiss%2C+EH&rft.au=Rollinger%2C+JM&rft.au=Schuster%2C+D&rft.au=Breuss%2C+JM&rft.au=Bochkov%2C+V&rft.au=Mihovilovic%2C+MD&rft.au=Kopp%2C+B&rft.au=Bauer%2C+R&rft.au=Dirsch%2C+VM&rft.au=Stuppner%2C+H&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC4748402&rfr_id=info%3Asid%2Fen.wikipedia.org%3AComputer+simulation" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text">Mizukami, Koichi; Saito, Fumio; Baron, Michel. <a rel="nofollow" class="external text" href="http://pem.utbm.fr/materiaux_2002/file/pdf/AF01078.PDF">Study on grinding of pharmaceutical products with an aid of computer simulation</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110721023918/http://pem.utbm.fr/materiaux_2002/file/pdf/AF01078.PDF">Archived</a> 2011-07-21 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text">Mesly, Olivier (2015). <i>Creating Models in Psychological Research.</i> United States: Springer Psychology: 126 pages. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-319-15752-8" title="Special:BookSources/978-3-319-15752-8">978-3-319-15752-8</a></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWilenskyRand2007" class="citation journal cs1">Wilensky, Uri; Rand, William (2007). <a rel="nofollow" class="external text" href="http://jasss.soc.surrey.ac.uk/10/4/2.html">"Making Models Match: Replicating an Agent-Based Model"</a>. <i>Journal of Artificial Societies and Social Simulation</i>. <b>10</b> (4): 2.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Artificial+Societies+and+Social+Simulation&rft.atitle=Making+Models+Match%3A+Replicating+an+Agent-Based+Model&rft.volume=10&rft.issue=4&rft.pages=2&rft.date=2007&rft.aulast=Wilensky&rft.aufirst=Uri&rft.au=Rand%2C+William&rft_id=http%3A%2F%2Fjasss.soc.surrey.ac.uk%2F10%2F4%2F2.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AComputer+simulation" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWescott2013" class="citation book cs1">Wescott, Bob (2013). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=0SD1mgEACAAJ"><i>The Every Computer Performance Book, Chapter 7: Modeling Computer Performance</i></a>. <a href="/wiki/CreateSpace" title="CreateSpace">CreateSpace</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1482657753" title="Special:BookSources/978-1482657753"><bdi>978-1482657753</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Every+Computer+Performance+Book%2C+Chapter+7%3A+Modeling+Computer+Performance&rft.pub=CreateSpace&rft.date=2013&rft.isbn=978-1482657753&rft.aulast=Wescott&rft.aufirst=Bob&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D0SD1mgEACAAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3AComputer+simulation" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text">Baase, Sara. A Gift of Fire: Social, Legal, and Ethical Issues for Computing and the Internet. 3. Upper Saddle River: Prentice Hall, 2007. Pages 363–364. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-13-600848-8" title="Special:BookSources/0-13-600848-8">0-13-600848-8</a>.</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computer_simulation&action=edit&section=11" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Computer_simulations" class="extiw" title="commons:Category:Computer simulations">Computer simulations</a></span>.</div></div> </div> <ul><li>Young, Joseph and Findley, Michael. 2014. "Computational Modeling to Study Conflicts and Terrorism." <a rel="nofollow" class="external text" href="https://books.google.com/books?id=ENDpAwAAQBAJ&pg=PT23">Routledge Handbook of Research Methods in Military Studies</a> edited by Soeters, Joseph; Shields, Patricia and Rietjens, Sebastiaan. pp. 249–260. New York: Routledge,</li> <li>R. Frigg and S. Hartmann, <a rel="nofollow" class="external text" href="http://plato.stanford.edu/entries/models-science/">Models in Science</a>. Entry in the <i> <a href="/wiki/Stanford_Encyclopedia_of_Philosophy" title="Stanford Encyclopedia of Philosophy">Stanford Encyclopedia of Philosophy</a></i>.</li> <li>E. Winsberg <a rel="nofollow" class="external text" href="http://plato.stanford.edu/entries/simulations-science/">Simulation in Science</a>. Entry in the <i> <a href="/wiki/Stanford_Encyclopedia_of_Philosophy" title="Stanford Encyclopedia of Philosophy">Stanford Encyclopedia of Philosophy</a></i>.</li> <li>S. Hartmann, <a rel="nofollow" class="external text" href="http://philsci-archive.pitt.edu/archive/00002412/">The World as a Process: Simulations in the Natural and Social Sciences</a>, in: R. Hegselmann et al. (eds.), <i>Modelling and Simulation in the Social Sciences from the Philosophy of Science Point of View</i>, Theory and Decision Library. Dordrecht: <a href="/wiki/Kluwer" class="mw-redirect" title="Kluwer">Kluwer</a> 1996, 77–100.</li> <li>E. Winsberg, <i>Science in the Age of Computer Simulation</i>. Chicago: <a href="/wiki/University_of_Chicago_Press" title="University of Chicago Press">University of Chicago Press</a>, 2010.</li> <li>P. Humphreys, <i>Extending Ourselves: Computational Science, Empiricism, and Scientific Method</i>. Oxford: <a href="/wiki/Oxford_University_Press" title="Oxford University Press">Oxford University Press</a>, 2004.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJames_J._Nutaro2011" class="citation book cs1">James J. Nutaro (2011). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=WZceCd74GRcC"><i>Building Software for Simulation: Theory and Algorithms, with Applications in C++</i></a>. John Wiley & Sons. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-118-09945-2" title="Special:BookSources/978-1-118-09945-2"><bdi>978-1-118-09945-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Building+Software+for+Simulation%3A+Theory+and+Algorithms%2C+with+Applications+in+C%2B%2B&rft.pub=John+Wiley+%26+Sons&rft.date=2011&rft.isbn=978-1-118-09945-2&rft.au=James+J.+Nutaro&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DWZceCd74GRcC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AComputer+simulation" class="Z3988"></span></li> <li>Desa, W. L. H. M., Kamaruddin, S., & Nawawi, M. K. M. (2012). Modeling of Aircraft Composite Parts Using Simulation. Advanced Material Research, 591–593, 557–560.</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computer_simulation&action=edit&section=12" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://www.lib.ncsu.edu/findingaids/mc00488">Guide to the Computer Simulation Oral History Archive 2003-2018</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output 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