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vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Modellelementer"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Modellelementer</span> </div> </a> <ul id="toc-Modellelementer-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Modelleringsprosessen" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Modelleringsprosessen"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Modelleringsprosessen</span> </div> </a> <ul id="toc-Modelleringsprosessen-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Modellkarakterisering" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Modellkarakterisering"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Modellkarakterisering</span> </div> </a> <button aria-controls="toc-Modellkarakterisering-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Vis/skjul underseksjonen Modellkarakterisering</span> </button> <ul id="toc-Modellkarakterisering-sublist" class="vector-toc-list"> <li id="toc-Analytiske_og_numeriske_modeller" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Analytiske_og_numeriske_modeller"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Analytiske og numeriske modeller</span> </div> </a> <ul id="toc-Analytiske_og_numeriske_modeller-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Deterministiske_og_stokastiske_modeller" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Deterministiske_og_stokastiske_modeller"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Deterministiske og stokastiske modeller</span> </div> </a> <ul id="toc-Deterministiske_og_stokastiske_modeller-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lineære_og_ikke-lineære_modeller" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Lineære_og_ikke-lineære_modeller"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Lineære og ikke-lineære modeller</span> </div> </a> <ul id="toc-Lineære_og_ikke-lineære_modeller-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Statiske_og_dynamiske_modeller" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Statiske_og_dynamiske_modeller"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Statiske og dynamiske modeller</span> </div> </a> <ul id="toc-Statiske_og_dynamiske_modeller-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Stasjonære_og_ikke-stasjonære_modeller" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Stasjonære_og_ikke-stasjonære_modeller"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.5</span> <span>Stasjonære og ikke-stasjonære modeller</span> </div> </a> <ul id="toc-Stasjonære_og_ikke-stasjonære_modeller-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Dimensjonsanalyse" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Dimensjonsanalyse"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Dimensjonsanalyse</span> </div> </a> <ul id="toc-Dimensjonsanalyse-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Eksempler_på_matematiske_modeller" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Eksempler_på_matematiske_modeller"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Eksempler på matematiske modeller</span> </div> </a> <ul id="toc-Eksempler_på_matematiske_modeller-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Referanser" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Referanser"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Referanser</span> </div> </a> <ul id="toc-Referanser-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Eksterne_lenker" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Eksterne_lenker"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Eksterne lenker</span> </div> </a> <ul id="toc-Eksterne_lenker-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="Innhold" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Innholdsfortegnelse" > <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="Vis/skjul innholdsfortegnelsen" > <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">Vis/skjul innholdsfortegnelsen</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">Matematisk modell</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" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Gå til en artikkel på et annet språk. Tilgjengelig på 56 språk" > <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-56" 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">56 språk</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Matematisk_modell" title="Matematisk modell – norsk nynorsk" lang="nn" hreflang="nn" data-title="Matematisk modell" data-language-autonym="Norsk nynorsk" data-language-local-name="norsk nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Model_(matematik)" title="Model (matematik) – dansk" lang="da" hreflang="da" data-title="Model (matematik)" data-language-autonym="Dansk" data-language-local-name="dansk" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Matematisk_modell" title="Matematisk modell – svensk" lang="sv" hreflang="sv" data-title="Matematisk modell" data-language-autonym="Svenska" data-language-local-name="svensk" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%86%D9%85%D9%88%D8%B0%D8%AC_%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A" title="نموذج رياضي – arabisk" lang="ar" hreflang="ar" data-title="نموذج رياضي" data-language-autonym="العربية" data-language-local-name="arabisk" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Riyazi_modell%C9%99%C5%9Fdirm%C9%99" title="Riyazi modelləşdirmə – aserbajdsjansk" lang="az" hreflang="az" data-title="Riyazi modelləşdirmə" data-language-autonym="Azərbaycanca" data-language-local-name="aserbajdsjansk" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B8_%D0%BC%D0%BE%D0%B4%D0%B5%D0%BB" title="Математически модел – bulgarsk" lang="bg" hreflang="bg" data-title="Математически модел" data-language-autonym="Български" data-language-local-name="bulgarsk" 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/Model_matem%C3%A0tic" title="Model matemàtic – katalansk" lang="ca" hreflang="ca" data-title="Model matemàtic" data-language-autonym="Català" data-language-local-name="katalansk" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%C4%83%D0%BB%D0%BB%C4%83_%D0%BC%D0%BE%D0%B4%D0%B5%D0%BB%D1%8C" title="Математикăллă модель – tsjuvasjisk" lang="cv" hreflang="cv" data-title="Математикăллă модель" data-language-autonym="Чӑвашла" data-language-local-name="tsjuvasjisk" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Matematick%C3%BD_model" title="Matematický model – tsjekkisk" lang="cs" hreflang="cs" data-title="Matematický model" data-language-autonym="Čeština" data-language-local-name="tsjekkisk" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Mathematisches_Modell" title="Mathematisches Modell – tysk" lang="de" hreflang="de" data-title="Mathematisches Modell" data-language-autonym="Deutsch" data-language-local-name="tysk" 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/Matemaatiline_mudel" title="Matemaatiline mudel – estisk" lang="et" hreflang="et" data-title="Matemaatiline mudel" data-language-autonym="Eesti" data-language-local-name="estisk" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Mathematical_model" title="Mathematical model – engelsk" lang="en" hreflang="en" data-title="Mathematical model" data-language-autonym="English" data-language-local-name="engelsk" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Modelo_matem%C3%A1tico" title="Modelo matemático – spansk" lang="es" hreflang="es" data-title="Modelo matemático" data-language-autonym="Español" data-language-local-name="spansk" 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/Matematika_modelo" title="Matematika modelo – esperanto" lang="eo" hreflang="eo" data-title="Matematika modelo" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Eredu_matematiko" title="Eredu matematiko – baskisk" lang="eu" hreflang="eu" data-title="Eredu matematiko" data-language-autonym="Euskara" data-language-local-name="baskisk" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D8%AF%D9%84_%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C" title="مدل ریاضی – persisk" lang="fa" hreflang="fa" data-title="مدل ریاضی" data-language-autonym="فارسی" data-language-local-name="persisk" 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/Mod%C3%A8le_math%C3%A9matique" title="Modèle mathématique – fransk" lang="fr" hreflang="fr" data-title="Modèle mathématique" data-language-autonym="Français" data-language-local-name="fransk" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Samhail_mhatamaitici%C3%BAil" title="Samhail mhatamaiticiúil – irsk" lang="ga" hreflang="ga" data-title="Samhail mhatamaiticiúil" data-language-autonym="Gaeilge" data-language-local-name="irsk" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Modelo_matem%C3%A1tico" title="Modelo matemático – galisisk" lang="gl" hreflang="gl" data-title="Modelo matemático" data-language-autonym="Galego" data-language-local-name="galisisk" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%88%98%ED%95%99%EC%A0%81_%EB%AA%A8%EB%8D%B8" title="수학적 모델 – koreansk" lang="ko" hreflang="ko" data-title="수학적 모델" data-language-autonym="한국어" data-language-local-name="koreansk" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%84%D5%A1%D5%A9%D5%A5%D5%B4%D5%A1%D5%BF%D5%AB%D5%AF%D5%A1%D5%AF%D5%A1%D5%B6_%D5%B4%D5%B8%D5%A4%D5%A5%D5%AC" title="Մաթեմատիկական մոդել – armensk" lang="hy" hreflang="hy" data-title="Մաթեմատիկական մոդել" data-language-autonym="Հայերեն" data-language-local-name="armensk" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4%E0%A5%80%E0%A4%AF_%E0%A4%AE%E0%A5%89%E0%A4%A1%E0%A4%B2" title="गणितीय मॉडल – hindi" lang="hi" hreflang="hi" data-title="गणितीय मॉडल" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Matemati%C4%8Dki_model" title="Matematički model – kroatisk" lang="hr" hreflang="hr" data-title="Matematički model" data-language-autonym="Hrvatski" data-language-local-name="kroatisk" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Matematikala_modelo" title="Matematikala modelo – ido" lang="io" hreflang="io" data-title="Matematikala modelo" 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/Model_matematika" title="Model matematika – indonesisk" lang="id" hreflang="id" data-title="Model matematika" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesisk" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Modello_matematico" title="Modello matematico – italiensk" lang="it" hreflang="it" data-title="Modello matematico" data-language-autonym="Italiano" data-language-local-name="italiensk" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%95%D7%93%D7%9C_%D7%9E%D7%AA%D7%9E%D7%98%D7%99" title="מודל מתמטי – hebraisk" lang="he" hreflang="he" data-title="מודל מתמטי" data-language-autonym="עברית" data-language-local-name="hebraisk" 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%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%D0%BB%D1%8B%D2%9B_%D0%BC%D0%BE%D0%B4%D0%B5%D0%BB%D1%8C%D0%B4%D0%B5%D1%83" title="Математикалық модельдеу – kasakhisk" lang="kk" hreflang="kk" data-title="Математикалық модельдеу" data-language-autonym="Қазақша" data-language-local-name="kasakhisk" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BB%81%E0%BA%9A%E0%BA%9A%E0%BA%88%E0%BA%B3%E0%BA%A5%E0%BA%AD%E0%BA%87%E0%BA%97%E0%BA%B2%E0%BA%87%E0%BA%84%E0%BA%B0%E0%BA%99%E0%BA%B4%E0%BA%94%E0%BA%AA%E0%BA%B2%E0%BA%94" title="ແບບຈຳລອງທາງຄະນິດສາດ – laotisk" lang="lo" hreflang="lo" data-title="ແບບຈຳລອງທາງຄະນິດສາດ" data-language-autonym="ລາວ" data-language-local-name="laotisk" class="interlanguage-link-target"><span>ລາວ</span></a></li><li class="interlanguage-link interwiki-lt badge-Q70894304 mw-list-item" title=""><a href="https://lt.wikipedia.org/wiki/Matematinis_modelis" title="Matematinis modelis – litauisk" lang="lt" hreflang="lt" data-title="Matematinis modelis" data-language-autonym="Lietuvių" data-language-local-name="litauisk" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Matematikai_modell" title="Matematikai modell – ungarsk" lang="hu" hreflang="hu" data-title="Matematikai modell" data-language-autonym="Magyar" data-language-local-name="ungarsk" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Model_matematik" title="Model matematik – malayisk" lang="ms" hreflang="ms" data-title="Model matematik" data-language-autonym="Bahasa Melayu" data-language-local-name="malayisk" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA_%D0%B7%D0%B0%D0%B3%D0%B2%D0%B0%D1%80" title="Математик загвар – mongolsk" lang="mn" hreflang="mn" data-title="Математик загвар" data-language-autonym="Монгол" data-language-local-name="mongolsk" 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/Wiskundig_model" title="Wiskundig model – nederlandsk" lang="nl" hreflang="nl" data-title="Wiskundig model" data-language-autonym="Nederlands" data-language-local-name="nederlandsk" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E6%95%B0%E7%90%86%E3%83%A2%E3%83%87%E3%83%AB" title="数理モデル – japansk" lang="ja" hreflang="ja" data-title="数理モデル" data-language-autonym="日本語" data-language-local-name="japansk" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Matematik_model" title="Matematik model – usbekisk" lang="uz" hreflang="uz" data-title="Matematik model" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="usbekisk" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Modelowanie_matematyczne" title="Modelowanie matematyczne – polsk" lang="pl" hreflang="pl" data-title="Modelowanie matematyczne" data-language-autonym="Polski" data-language-local-name="polsk" 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/Modelo_(matem%C3%A1tica)" title="Modelo (matemática) – portugisisk" lang="pt" hreflang="pt" data-title="Modelo (matemática)" data-language-autonym="Português" data-language-local-name="portugisisk" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-kaa mw-list-item"><a href="https://kaa.wikipedia.org/wiki/Matematikal%C4%B1q_modellestiriw" title="Matematikalıq modellestiriw – karakalpakisk" lang="kaa" hreflang="kaa" data-title="Matematikalıq modellestiriw" data-language-autonym="Qaraqalpaqsha" data-language-local-name="karakalpakisk" class="interlanguage-link-target"><span>Qaraqalpaqsha</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Modelare_matematic%C4%83" title="Modelare matematică – rumensk" lang="ro" hreflang="ro" data-title="Modelare matematică" data-language-autonym="Română" data-language-local-name="rumensk" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0%D1%8F_%D0%BC%D0%BE%D0%B4%D0%B5%D0%BB%D1%8C" title="Математическая модель – russisk" lang="ru" hreflang="ru" data-title="Математическая модель" data-language-autonym="Русский" data-language-local-name="russisk" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Mathematical_model" title="Mathematical model – skotsk" lang="sco" hreflang="sco" data-title="Mathematical model" data-language-autonym="Scots" data-language-local-name="skotsk" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Mathematical_model" title="Mathematical model – enkel engelsk" lang="en-simple" hreflang="en-simple" data-title="Mathematical model" data-language-autonym="Simple English" data-language-local-name="enkel engelsk" 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/Matematick%C3%BD_model" title="Matematický model – slovakisk" lang="sk" hreflang="sk" data-title="Matematický model" data-language-autonym="Slovenčina" data-language-local-name="slovakisk" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D1%87%D0%BA%D0%B8_%D0%BC%D0%BE%D0%B4%D0%B5%D0%BB" title="Математички модел – serbisk" lang="sr" hreflang="sr" data-title="Математички модел" data-language-autonym="Српски / srpski" data-language-local-name="serbisk" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Matemati%C4%8Dki_model" title="Matematički model – serbokroatisk" lang="sh" hreflang="sh" data-title="Matematički model" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbokroatisk" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Matemaattinen_malli" title="Matemaattinen malli – finsk" lang="fi" hreflang="fi" data-title="Matemaattinen malli" data-language-autonym="Suomi" data-language-local-name="finsk" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Modelong_matematikal" title="Modelong matematikal – tagalog" lang="tl" hreflang="tl" data-title="Modelong matematikal" data-language-autonym="Tagalog" data-language-local-name="tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%95%E0%AE%A3%E0%AE%BF%E0%AE%A4_%E0%AE%AE%E0%AE%BE%E0%AE%A4%E0%AE%BF%E0%AE%B0%E0%AE%BF" title="கணித மாதிரி – tamil" lang="ta" hreflang="ta" data-title="கணித மாதிரி" data-language-autonym="தமிழ்" data-language-local-name="tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%81%E0%B8%9A%E0%B8%9A%E0%B8%88%E0%B8%B3%E0%B8%A5%E0%B8%AD%E0%B8%87%E0%B8%97%E0%B8%B2%E0%B8%87%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C" title="แบบจำลองทางคณิตศาสตร์ – thai" lang="th" hreflang="th" data-title="แบบจำลองทางคณิตศาสตร์" data-language-autonym="ไทย" data-language-local-name="thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Matematiksel_model" title="Matematiksel model – tyrkisk" lang="tr" hreflang="tr" data-title="Matematiksel model" data-language-autonym="Türkçe" data-language-local-name="tyrkisk" 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%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D1%87%D0%BD%D0%B0_%D0%BC%D0%BE%D0%B4%D0%B5%D0%BB%D1%8C" title="Математична модель – ukrainsk" lang="uk" hreflang="uk" data-title="Математична модель" data-language-autonym="Українська" data-language-local-name="ukrainsk" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C%D8%A7%D8%AA%DB%8C_%D9%86%D9%85%D9%88%D9%86%DB%81" title="ریاضیاتی نمونہ – urdu" lang="ur" hreflang="ur" data-title="ریاضیاتی نمونہ" data-language-autonym="اردو" data-language-local-name="urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/M%C3%B4_h%C3%ACnh_to%C3%A1n_h%E1%BB%8Dc" title="Mô hình toán học – vietnamesisk" lang="vi" hreflang="vi" data-title="Mô hình toán học" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamesisk" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link 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andre prosjekter </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Mathematical_models" hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q486902" title="Lenke til koblet dataregisterelement [g]" accesskey="g"><span>Wikidata-element</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Sideverktøy"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Utseende"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Utseende</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">flytt til sidefeltet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">skjul</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Fra Wikipedia, den frie encyklopedi</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="nb" dir="ltr"><p>En <b>matematisk modell</b> er en <a href="/wiki/Modell_(vitenskap)" class="mw-redirect" title="Modell (vitenskap)">vitenskapelig modell</a> uttrykt i et formelt <a href="/wiki/Matematikk" title="Matematikk">matematisk</a> språk. En modell er et fragment av en matematisk teori som representerer en del av virkeligheten, for eksempel et fysisk system eller objekt.<sup id="cite_ref-COLLINS_1-0" class="reference"><a href="#cite_note-COLLINS-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-SHIER_2-0" class="reference"><a href="#cite_note-SHIER-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>Fra en matematisk modell er en i stand til å trekke matematiske og kvantitative slutninger om fenomenet som studeres. Matematiske modeller brukes derfor i nær sagt alle former for vitenskap: naturvitenskap, samfunnsfag, medisin og musikk.<sup id="cite_ref-SIAM1_3-0" class="reference"><a href="#cite_note-SIAM1-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Særlig er modeller i <a href="/wiki/Fysikk" title="Fysikk">fysikk</a> svært ofte uttrykt i et matematisk språk.<sup id="cite_ref-CH_4-0" class="reference"><a href="#cite_note-CH-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>Matematiske modeller studeres særskilt i <a href="/wiki/Anvendt_matematikk" title="Anvendt matematikk">anvendt matematikk</a>, en vitenskapsgren der en fokuserer på anvendelser av matematikk i andre fag. </p><p>I mange tilfeller kan en og samme matematiske modell fungere for mange ulike problemstillinger fra den virkelige verden. Dette kan gi mulighet til å overføre kjent teori til nye problemstillinger og til å sammenligne oppførsel til helt ulike systemer. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Modellelementer">Modellelementer</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematisk_modell&veaction=edit&section=1" title="Rediger avsnitt: Modellelementer" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematisk_modell&action=edit&section=1" title="Rediger kildekoden til seksjonen Modellelementer"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>En matematisk modell vil typisk bestå av et sett av matematiske relasjoner mellom objekter, definert for eksempel som <a href="/wiki/Ligning_(matematikk)" title="Ligning (matematikk)">ligninger</a>, <a href="/wiki/Ulikhet_(matematikk)" title="Ulikhet (matematikk)">ulikheter</a> og <a href="/wiki/Funksjon_(matematikk)" title="Funksjon (matematikk)">funksjoner</a>. Objektene kan være alle typer matematiske størrelser, som <a href="/wiki/Skalar" title="Skalar">skalarer</a>, <a href="/wiki/Vektor_(matematikk)" title="Vektor (matematikk)">vektorer</a>, <a href="/wiki/Matrise" title="Matrise">matriser</a>, <a href="/wiki/Tensor" title="Tensor">tensorer</a>, <a href="/wiki/Funksjon_(matematikk)" title="Funksjon (matematikk)">funksjoner</a>, <a href="/wiki/Sannsynlighetsfordeling" title="Sannsynlighetsfordeling">sannsynlighetsfordelinger</a> osv. </p><p>I mange modeller som ser på endringer i en eller flere størrelser spiller <a href="/wiki/Differensialligning" title="Differensialligning">differensialligninger</a> en viktig rolle, ligninger som beskriver sammenheng mellom en funksjon og endringer i denne. Endringer kan ofte være variasjoner i tid og rom, men kan også være et resultat av <a href="/wiki/Kausalitet" title="Kausalitet">kausalitet</a>, for eksempel at en endring i væsketrykket avhenger av en endring i temperaturen. </p><p>Tilstanden til systemet som studeres kan beskrives av et sett av <a href="/wiki/Variabel" title="Variabel">variable</a>, ofte karakterisert som <i>tilstandsvariable</i>. Mengden av verdier disse variablene kan ta kalles <i>tilstandsrommet</i> for systemet. En matematisk modell kan dermed beskrives som en formell struktur av tilstandsvariable. En modell blir ofte brukt til å finne tilstandsvariabler som ukjente i et ligningssystem. </p><p>I tillegg til tilstandsvariable vil en modell ofte inneholde modellkonstanter eller <a href="/wiki/Parameter" title="Parameter">parametre</a> som definerer systemet. </p> <div class="mw-heading mw-heading2"><h2 id="Modelleringsprosessen">Modelleringsprosessen</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematisk_modell&veaction=edit&section=2" title="Rediger avsnitt: Modelleringsprosessen" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematisk_modell&action=edit&section=2" title="Rediger kildekoden til seksjonen Modelleringsprosessen"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Matematisk modellering som arbeidsprosess kan i seg selv beskrives med en idealisert modell, og to ulike modeller er her kalt <i>Modell A</i> og <i>Modell B</i>. </p><p>I <i>Model A</i> deler en prosessen inn i seks ulike steg:<sup id="cite_ref-SIAM1_3-1" class="reference"><a href="#cite_note-SIAM1-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <ol><li>Identifikasjon: I det første steget må en identifisere at det er et problem som trenger løsning og beskrive problemstillingen. En må også bestemme seg for hva en ønsker å oppnå med en modell.</li> <li>Formulering: Problemet må bli gitt en matematisk formulering.</li> <li>Løsning: Den matematiske formuleringen er som oftest i form av en problemstilling som krever en løsning. Svært ofte vil en måtte nøye seg med en tilnærmet løsning.</li> <li>Beregning: En eksakt eller tilnærmet løsning vil ofte kreve en numerisk beregning, som oftest utført ved hjelp av en <a href="/wiki/Datamaskin" title="Datamaskin">datamaskin</a>.</li> <li>Kommunikasjon: I det siste steget må det beregnede svaret tolkes og kommuniseres til den eller de som trenger å kjenne resultatet.</li></ol> <p>En modellberegning utført på en datamaskin kalles gjerne en <a href="/wiki/Datasimulering" title="Datasimulering">simulering</a>. </p><p><i>Modell B</i> inneholder de samme stegene i en noe mer komprimert form:<sup id="cite_ref-SHIER_2-1" class="reference"><a href="#cite_note-SHIER-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <ol><li>Formulering av problemet i den virkelige verden.</li> <li>Formulering av den matematiske modellen.</li> <li>Konstruksjon av en matematiske løsning.</li> <li>Tolking av den matematiske løsningen i den virkelige verden.</li></ol> <p>Både <i>Modell A</i> og <i>Modell B</i> framhever den iterative karakteren av modelleringsprosessen, der en ofte må gå fram og tilbake mellom ulike steg. Begge modeller understreker også betydningen av tolkning av de matematiske resultatene sett i relasjon til den opprinnelige problemstillingen. Verifikasjonsprosessen som må gjøres for å prøve ut gyldigheten til modellen, er en del av dette tolkningssteget. </p> <div class="mw-heading mw-heading2"><h2 id="Modellkarakterisering">Modellkarakterisering</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematisk_modell&veaction=edit&section=3" title="Rediger avsnitt: Modellkarakterisering" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematisk_modell&action=edit&section=3" title="Rediger kildekoden til seksjonen Modellkarakterisering"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Matematiske modeller kan karakteriseres på svært mange forskjellige måter, og noen måter er skissert i det følgende avsnittet. </p> <div class="mw-heading mw-heading3"><h3 id="Analytiske_og_numeriske_modeller">Analytiske og numeriske modeller</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematisk_modell&veaction=edit&section=4" title="Rediger avsnitt: Analytiske og numeriske modeller" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematisk_modell&action=edit&section=4" title="Rediger kildekoden til seksjonen Analytiske og numeriske modeller"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>En <i>numerisk modell</i> er en modell som bruker verktøy fra <a href="/wiki/Numerisk_analyse" title="Numerisk analyse">numerisk analyse</a> til å finne tilnærmede løsninger til et sett av modelligninger. Løsninger av modelligningene i en numerisk modell vil være numeriske verdier eller <i>tall</i>. </p><p>I motsetning til dette er en <i>analytisk modell</i> en modell der løsningen er beskrevet som matematiske objekter forskjellig fra tall, vanligvis i form av <a href="/wiki/Analytisk_funksjon" title="Analytisk funksjon">analytiske funksjoner</a>. </p><p>En numerisk modell vil som oftest være basert på en analytisk modell. </p> <div class="mw-heading mw-heading3"><h3 id="Deterministiske_og_stokastiske_modeller">Deterministiske og stokastiske modeller</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematisk_modell&veaction=edit&section=5" title="Rediger avsnitt: Deterministiske og stokastiske modeller" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematisk_modell&action=edit&section=5" title="Rediger kildekoden til seksjonen Deterministiske og stokastiske modeller"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>En <i>stokastisk modell</i> er en <a href="/w/index.php?title=Statistisk_modell&action=edit&redlink=1" class="new" title="Statistisk modell (ikke skrevet ennå)">statistisk modell</a> som inkluderer element av tilfeldighet, slik at det ikke er mulig å predikere oppførselen til modellen eksakt. [[Stokastiske prosess]er brukes for å modellere endringer eller fordelinger i det som observeres. I en <a href="/wiki/Determinisme" title="Determinisme">deterministisk</a> modell er det ingen element av tilfeldighet. </p> <div class="mw-heading mw-heading3"><h3 id="Lineære_og_ikke-lineære_modeller"><span id="Line.C3.A6re_og_ikke-line.C3.A6re_modeller"></span>Lineære og ikke-lineære modeller</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematisk_modell&veaction=edit&section=6" title="Rediger avsnitt: Lineære og ikke-lineære modeller" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematisk_modell&action=edit&section=6" title="Rediger kildekoden til seksjonen Lineære og ikke-lineære modeller"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>En lineær modell er en modell der tilstandsvariablene inngår <a href="/wiki/Linearitet" title="Linearitet">lineært</a> i modellrelasjonene. Motsetningen er en ikke-lineær modell. Linearitet uttrykkes ofte som <a href="/wiki/Proporsjonalitet" title="Proporsjonalitet">proporsjonalitet</a>. </p><p>Et eksempel på en lineær modell for bølgeforplatning i en romdimensjon er gitt ved <a href="/wiki/B%C3%B8lgeligning" title="Bølgeligning">bølgeligningen</a> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u_{tt}-cu_{xx}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mi>t</mi> </mrow> </msub> <mo>−</mo> <mi>c</mi> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u_{tt}-cu_{xx}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d11c384c08ace88428071d6f219af3a9995a88b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.3ex; height:2.509ex;" alt="{\displaystyle u_{tt}-cu_{xx}=0}" /></span></dd></dl> <p>En ikke-lineær modell for forplantning av [sjokkbølge]]r kan være basert på <a href="/w/index.php?title=Burgers%27_ligning&action=edit&redlink=1" class="new" title="Burgers' ligning (ikke skrevet ennå)">Burgers' ligning</a>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u_{t}-uu_{x}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mo>−</mo> <mi>u</mi> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u_{t}-uu_{x}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9007d8311a174f1f071ef5df5232f9e0e0efabd6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.089ex; height:2.509ex;" alt="{\displaystyle u_{t}-uu_{x}=0}" /></span></dd></dl> <p>En modell med differensialligninger kalles også <i>kvasilineær</i> dersom modellen er lineær i den høyeste-ordens-deriverte av den ukjente funksjonen.<sup id="cite_ref-TYN_5-0" class="reference"><a href="#cite_note-TYN-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Statiske_og_dynamiske_modeller">Statiske og dynamiske modeller</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematisk_modell&veaction=edit&section=7" title="Rediger avsnitt: Statiske og dynamiske modeller" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematisk_modell&action=edit&section=7" title="Rediger kildekoden til seksjonen Statiske og dynamiske modeller"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>En <i>dynamisk</i> modell er en matematisk modell som involverer bevegelse. Motsetningen er en <i>statisk</i> modell, der ting er i likevekt. </p><p>I <a href="/wiki/Statikk" title="Statikk">statikk</a> studerer en forholdet mellom legemer i likevekt og i <a href="/wiki/Hydrostatikk" title="Hydrostatikk">hydrostatikk</a> forholdet mellom væsker i ro. <a href="/wiki/Hydrodynamikk" title="Hydrodynamikk">Hydrodynamikk</a> er et fagfelt der en bruker modeller for væsker i bevegelse. </p> <div class="mw-heading mw-heading3"><h3 id="Stasjonære_og_ikke-stasjonære_modeller"><span id="Stasjon.C3.A6re_og_ikke-stasjon.C3.A6re_modeller"></span>Stasjonære og ikke-stasjonære modeller</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematisk_modell&veaction=edit&section=8" title="Rediger avsnitt: Stasjonære og ikke-stasjonære modeller" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematisk_modell&action=edit&section=8" title="Rediger kildekoden til seksjonen Stasjonære og ikke-stasjonære modeller"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>I en <i>stasjonær modell</i> forsøker en å representere noe som ikke endrer seg med tid, for eksempel fordi ting er i likevekt eller fordi bevegelsen ikke endrer seg med tiden. I en ikke-stasjonær modell vil tilstandsvariablene endre seg med tiden. </p> <div class="mw-heading mw-heading2"><h2 id="Dimensjonsanalyse">Dimensjonsanalyse</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematisk_modell&veaction=edit&section=9" title="Rediger avsnitt: Dimensjonsanalyse" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematisk_modell&action=edit&section=9" title="Rediger kildekoden til seksjonen Dimensjonsanalyse"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>I <a href="/w/index.php?title=Dimensjonsanalyse&action=edit&redlink=1" class="new" title="Dimensjonsanalyse (ikke skrevet ennå)">dimensjonsanalyse</a> av en matematisk modell identifiseres grunnleggende dimensjoner til modellstørrelser relativt til grunnlegende størrelser som tid, lengde, temperatur og elektrisk ladning.<sup id="cite_ref-NORM_6-0" class="reference"><a href="#cite_note-NORM-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> For eksempel er dimensjonen til <i>hastighet</i> med hensyn på lengde lik 1 og med hensyn på tid lik -1. Dimensjonseksponentene er heltall uten benevning som er uavhengige av måleenheter. Grunnleggende funksjoner som <a href="/wiki/Trigonometrisk_funksjon" title="Trigonometrisk funksjon">trigonometriske funksjoner</a> og <a href="/wiki/Eksponentialfunksjon" title="Eksponentialfunksjon">eksponentialfunksjonen</a> har dimensjon null og må ha argument med dimensjon null. </p><p>For et ligningsledd som består av flere størrelser kan en regne ut en totaleksponent ved å summere bidragene fra alle størrelsene som inngår. I en flerleddet ligning må alle leddene ha samme dimensjon. </p><p>Ved hjelp av dimensjonseksponentene kan en analysere en modell både for å se om det er konsistent og for å avklare relasjoner mellom størrelser i modellen. </p><p>Enhver fysikalsk ligning kan skaleres, slik at den bare inneholder dimensjonsløse størrelser. I tillegg til dimensjonsløse tilstandsvariable vil skalerte ligninger typisk inneholde fundamentale dimensjonsløse tall eller parametre, definert som kombinasjoner av fysiske, målbare størrelser. De dimensjonsløse tallene er ofte mål på forholdet mellom ulike faktorer som påvirker modellen, og tallene er svært viktige i all analyse av modellen. En rekke dimensjonsløse tall er definerte med standard navn og kjente eksempler er <a href="/wiki/Mach" title="Mach">Mach-tallet</a>, <a href="/w/index.php?title=P%C3%A9clet-tall&action=edit&redlink=1" class="new" title="Péclet-tall (ikke skrevet ennå)">Péclet-tallet</a>, <a href="/wiki/Reynoldstall" title="Reynoldstall">Reynoldstallet</a> og <a href="/wiki/Richardson-tallet" title="Richardson-tallet">Richardson-tallet</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Eksempler_på_matematiske_modeller"><span id="Eksempler_p.C3.A5_matematiske_modeller"></span>Eksempler på matematiske modeller</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematisk_modell&veaction=edit&section=10" title="Rediger avsnitt: Eksempler på matematiske modeller" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematisk_modell&action=edit&section=10" title="Rediger kildekoden til seksjonen Eksempler på matematiske modeller"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Global_klimamodell" title="Global klimamodell">Global klimamodell</a></li> <li><a href="/wiki/MODAG" title="MODAG">MODAG</a>-modellen for norsk økonomi</li> <li><a href="/wiki/Numerisk_fluiddynamikk" title="Numerisk fluiddynamikk">Numerisk fluiddynamikk</a></li> <li><a href="/wiki/Numerisk_v%C3%A6rvarsling" title="Numerisk værvarsling">Numerisk værvarsling</a></li> <li><a href="/wiki/Reservoarsimulering" title="Reservoarsimulering">Reservoarsimulering</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Referanser">Referanser</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematisk_modell&veaction=edit&section=11" title="Rediger avsnitt: Referanser" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematisk_modell&action=edit&section=11" title="Rediger kildekoden til seksjonen Referanser"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-COLLINS-1"><b><a href="#cite_ref-COLLINS_1-0">^</a></b> <span class="reference-text"><cite class="citation book">E.J.Borowski, J.M.Borwein (1989). <i>Dictionary of mathematics</i>. Glasgow: Collins. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/Spesial:Bokkilder/0-00-434347-6" title="Spesial:Bokkilder/0-00-434347-6">0-00-434347-6</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fno.wikipedia.org%3AMatematisk+modell&rft.au=E.J.Borowski%2C+J.M.Borwein&rft.btitle=Dictionary+of+mathematics&rft.date=1989&rft.genre=book&rft.isbn=0-00-434347-6&rft.place=Glasgow&rft.pub=Collins&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-SHIER-2"><b>^</b> <a href="#cite_ref-SHIER_2-0"><sup>a</sup></a> <a href="#cite_ref-SHIER_2-1"><sup>b</sup></a> <span class="reference-text"><cite class="citation book">D.R.Shier, K.T.Wallenius, red. (2000). <a rel="nofollow" class="external text" href="https://books.google.no/books?id=kYZ8dXdgsloC&printsec=frontcover&hl=no#v=onepage&q&f=false"><i>Applied mathematical modelling: A multidisciplinary approach</i></a>. London: Chapmann&Hall/CRC. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/Spesial:Bokkilder/1-58488-048-1" title="Spesial:Bokkilder/1-58488-048-1">1-58488-048-1</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fno.wikipedia.org%3AMatematisk+modell&rft.btitle=Applied+mathematical+modelling%3A+A+multidisciplinary+approach&rft.date=2000&rft.genre=book&rft.isbn=1-58488-048-1&rft.place=London&rft.pub=Chapmann%26Hall%2FCRC&rft_id=https%3A%2F%2Fbooks.google.no%2Fbooks%3Fid%3DkYZ8dXdgsloC%26printsec%3Dfrontcover%26hl%3Dno%23v%3Donepage%26q%26f%3Dfalse&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-SIAM1-3"><b>^</b> <a href="#cite_ref-SIAM1_3-0"><sup>a</sup></a> <a href="#cite_ref-SIAM1_3-1"><sup>b</sup></a> <span class="reference-text"><cite class="citation book">M.S.Klamkin, red. (1987). <a rel="nofollow" class="external text" href="https://books.google.no/books?id=QqIVL2F7_kUC&printsec=frontcover&hl=no#v=onepage&q&f=false"><i>Mathematical modelling: Classroom notes in applied mathematics</i></a>. SIAM. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/Spesial:Bokkilder/0-89871-204-1" title="Spesial:Bokkilder/0-89871-204-1">0-89871-204-1</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fno.wikipedia.org%3AMatematisk+modell&rft.btitle=Mathematical+modelling%3A+Classroom+notes+in+applied+mathematics&rft.date=1987&rft.genre=book&rft.isbn=0-89871-204-1&rft.pub=SIAM&rft_id=https%3A%2F%2Fbooks.google.no%2Fbooks%3Fid%3DQqIVL2F7_kUC%26printsec%3Dfrontcover%26hl%3Dno%23v%3Donepage%26q%26f%3Dfalse&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-CH-4"><b><a href="#cite_ref-CH_4-0">^</a></b> <span class="reference-text"><cite class="citation book">R.Courant, D.Hilbert (1924). <i>Methods of mathematical physics</i>. New York: Wiley. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/Spesial:Bokkilder/978-0471504474" title="Spesial:Bokkilder/978-0471504474">978-0471504474</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fno.wikipedia.org%3AMatematisk+modell&rft.au=R.Courant%2C+D.Hilbert&rft.btitle=Methods+of+mathematical+physics&rft.date=1924&rft.genre=book&rft.isbn=978-0471504474&rft.place=New+York&rft.pub=Wiley&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-TYN-5"><b><a href="#cite_ref-TYN_5-0">^</a></b> <span class="reference-text"><cite class="citation book">T.Myint-U (1973). <i>Partial differensial equations of mathematical physics</i>. New York: Elsevier. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/Spesial:Bokkilder/0-444-00132-8" title="Spesial:Bokkilder/0-444-00132-8">0-444-00132-8</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fno.wikipedia.org%3AMatematisk+modell&rft.au=T.Myint-U&rft.btitle=Partial+differensial+equations+of+mathematical+physics&rft.date=1973&rft.genre=book&rft.isbn=0-444-00132-8&rft.place=New+York&rft.pub=Elsevier&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-NORM-6"><b><a href="#cite_ref-NORM_6-0">^</a></b> <span class="reference-text"><cite class="citation book">K.B.Dysthe (1992). <i>Dimensjonsanalyse</i>. Tromsø: Universitetet i Tromsø. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/Spesial:Bokkilder/82-90487-74-6" title="Spesial:Bokkilder/82-90487-74-6">82-90487-74-6</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fno.wikipedia.org%3AMatematisk+modell&rft.au=K.B.Dysthe&rft.btitle=Dimensjonsanalyse&rft.date=1992&rft.genre=book&rft.isbn=82-90487-74-6&rft.place=Troms%C3%B8&rft.pub=Universitetet+i+Troms%C3%B8&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Eksterne_lenker">Eksterne lenker</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematisk_modell&veaction=edit&section=12" title="Rediger avsnitt: Eksterne lenker" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematisk_modell&action=edit&section=12" title="Rediger kildekoden til seksjonen Eksterne lenker"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Konkurranser i matematisk modellering: </p> <ul><li><a rel="nofollow" class="external text" href="https://m3challenge.siam.org/">m3challenge.siam.org</a> MathWork's Math Modeling Challenge (engelsk). Besøkt 27. november 2019.</li> <li><a rel="nofollow" class="external text" href="https://immchallenge.org/">immchallenge.org</a> The International Mathematical Modeling Challenge (engelsk). Besøkt 27. november 2019.</li> <li><a rel="nofollow" class="external text" href="https://www.comap.com/undergraduate/contests/mcm/">www.comap.com</a> Mathematical Contest in Modeling (engelsk). Besøkt 27. november 2019.</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r24994932">.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 .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist 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<div class="vector-sticky-header-icons"> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-talk-sticky-header" tabindex="-1" data-event-name="talk-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbles mw-ui-icon-wikimedia-speechBubbles"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-subject-sticky-header" tabindex="-1" data-event-name="subject-sticky-header"><span class="vector-icon mw-ui-icon-article mw-ui-icon-wikimedia-article"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-history-sticky-header" tabindex="-1" data-event-name="history-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-history 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