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From cavitation to astrophysics: Explicit solution of the spherical collapse equation - PubMed
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class="collections-new" name="collections" value="new" data-ga-category="save_share" data-ga-action="collections" data-ga-label="collections_radio_new"> <label for="collections-action-panel-new">Create a new collection</label> </li> <li> <input type="radio" id="collections-action-panel-existing" class="collections-existing" name="collections" value="existing" checked="true" data-ga-category="save_share" data-ga-action="collections" data-ga-label="collections_radio_existing"> <label for="collections-action-panel-existing">Add to an existing collection</label> </li> </ul> </div> <div class="controls-wrapper"> <div class="action-panel-control-wrap new-collections-controls"> <label for="collections-action-panel-add-to-new" class="action-panel-label required-field-asterisk"> Name your collection: </label> <input type="text" name="add-to-new-collection" id="collections-action-panel-add-to-new" class="collections-action-add-to-new" pattern="[^"&=<>\/]*" title="The following characters are not allowed in the Name field: "&=<>/" maxlength="100" data-ga-category="save_share" data-ga-action="create_collection" data-ga-label="non_favorties_collection"> <div class="collections-new-name-too-long usa-input-error-message selection-validation-message"> Name must be less than 100 characters </div> </div> <div class="action-panel-control-wrap existing-collections-controls"> <label for="collections-action-panel-add-to-existing" class="action-panel-label"> Choose a collection: </label> <select id="collections-action-panel-add-to-existing" class="action-panel-selector collections-action-add-to-existing" data-ga-category="save_share" data-ga-action="select_collection" data-ga-label="($('#collections-action-add-to-existing').val() === 'Favorites') ? 'Favorites' : 'non_favorites_collection'"> </select> <div class="collections-retry-load-on-error usa-input-error-message selection-validation-message"> Unable to load your collection due to an error<br> <a href="#">Please try again</a> </div> </div> </div> <div class="action-panel-actions"> <button class="action-panel-submit" type="submit" data-loading-label="Adding..." data-pinger-ignore data-ga-category="save_share" data-ga-action="collections" data-ga-label="add"> Add </button> <button class="action-panel-cancel" aria-label="Close 'Add to Collections' panel" ref="linksrc=close_collections_panel" aria-controls="collections-action-panel" aria-expanded="false" data-ga-category="save_share" data-ga-action="collections" data-ga-label="cancel"> Cancel </button> </div> </form> </div> </div> <div id="bibliography-action-panel" class="bibliography-action-panel action-panel in-progress-dots-panel" aria-hidden="true" data-bibliography-open-panel-enabled="false" data-bibliography-open-panel-url-hash="#open-bibliography-panel"> <div class="inner-wrap"> <h3 class="action-panel-heading"> Add to My Bibliography </h3> <form id="bibliography-action-panel-form" class="bibliography-action-panel-form action-panel-content action-form action-panel-smaller-selectors" data-add-to-bibliography-max-amount="100" data-add-to-bibliography-batch-size="10" data-bibliography-delegates-url="/list-bibliography-delegates/" data-add-to-bibliography-url="/add-to-bibliography/" data-get-article-ids-by-search-url="/get-article-ids-by-search/" data-mybib-root-url="https://www.ncbi.nlm.nih.gov/myncbi/collections/mybibliography/"> <input type="hidden" name="csrfmiddlewaretoken" value="wPqrKgBMwpRKYBv3H1cVoAVmKocIKMxlv1gk1YKH16A1tT7xs7dz8IFE2Pj7iWXH"> <div class="action-panel-control-wrap bibliographies-controls"> <div class="choice-group"> <ul class="bibliographies-action-add radio-group-items"> <li> <input name="bibliography" id="my-bibliography" class="my-bibliography" type="radio" checked/> <label for="my-bibliography">My Bibliography</label> </li> </ul> </div> </div> <div class="bibliographies-retry-load-on-error usa-input-error-message selection-validation-message"> Unable to load your delegates due to an error<br> <a href="#">Please try again</a> </div> <div class="action-panel-actions"> <button class="action-panel-submit" type="submit" data-loading-label="Adding..." data-pinger-ignore> Add </button> <button class="action-panel-cancel" aria-label="Close 'Add to bibliography' panel" ref="linksrc=close_bibliography_panel" aria-controls="bibliography-action-panel" aria-expanded="false" data-ga-category="save_share" data-ga-action="mybib" data-ga-label="cancel"> Cancel </button> </div> </form> </div> </div> <div id="saved-search-action-panel" class="saved-search-action-panel action-panel " aria-hidden="true" data-saved-search-open-panel-enabled="false" data-saved-search-open-panel-url-hash="#open-saved-search-panel"> <div class="inner-wrap"> <h2 class="action-panel-heading"> Your saved search </h2> <form id="saved-search-action-panel-form" class="saved-search-action-panel-form action-panel-content action-form" data-create-saved-search-url="/create-saved-search/" data-try-search-terms-url="/try-search-term/" data-saved-search-root-url="https://www.ncbi.nlm.nih.gov/myncbi/searches/"> <input type="hidden" name="csrfmiddlewaretoken" value="wPqrKgBMwpRKYBv3H1cVoAVmKocIKMxlv1gk1YKH16A1tT7xs7dz8IFE2Pj7iWXH"> <div class="action-panel-control-wrap"> <label for="saved-search-name" class="action-panel-label saved-search-name-label required-field-asterisk"> Name of saved search: </label> <input maxlength="200" type="text" name="saved-search-name" id="saved-search-name" class="saved-search-name" value="" required pattern="[^"&=<>\/]*" title="The following characters are not allowed in the Name field: "&=<>/"> </div> <div class="action-panel-control-wrap"> <label for="saved-search-term" class="action-panel-label required-field-asterisk"> Search terms: </label> <textarea name="saved-search-term" id="saved-search-term" class="saved-search-term" required></textarea> </div> <div class="test-search-term-wrap"> <a href="#" class="try-search-term">Test search terms</a> </div> <div class="choice-group action-panel-extra-margin-top"> <span class="action-panel-label" id="fieldset-label"> Would you like email updates of new search results? </span> <fieldset id="saved-search-alert" aria-describedby="fieldset-label"> <legend class="usa-sr-only">Saved Search Alert Radio Buttons</legend> <ul class="radio-group-items"> <li> <input type="radio" id="saved-search-alert-yes" class="saved-search-alert-yes" name="saved-search-alert" value="yes" checked> <label for="saved-search-alert-yes" class="action-panel-label">Yes</label> </li> <li> <input aria-label="No radio input" type="radio" id="saved-search-alert-no" class="saved-search-alert-no" name="saved-search-alert" value="no"> <label for="saved-search-alert-no" class="action-panel-label">No</label> </li> </ul> </fieldset> </div> <div class="alert-schedule-wrap"> <div class="action-panel-control-wrap"> <label class="action-panel-label"> Email: </label> <span aria-label="Email address" id="saved-search-email" class="action-panel-label"><span class="action-panel-label-bold"></span> (<a class="myncbi-account-settings" href="https://www.ncbi.nlm.nih.gov/account/settings/">change</a>)</span> </div> <div class="action-panel-control-wrap action-panel-extra-margin-top"> <label for="saved-search-frequency" class="action-panel-label"> Frequency: </label> <select id="saved-search-frequency" class="no-border-panel-selector saved-search-frequency"> <option value="monthly">Monthly</option> <option value="weekly">Weekly</option> <option value="daily">Daily</option> </select> </div> <div class="action-panel-control-wrap saved-search-monthly-additional"> <label for="saved-search-monthly-on-day" class="action-panel-label"> Which day? </label> <select id="saved-search-monthly-on-day" class="no-border-panel-selector"> <option value="Sunday">The first Sunday</option> <option value="Monday">The first Monday</option> <option value="Tuesday">The first Tuesday</option> <option value="Wednesday">The first Wednesday</option> <option value="Thursday">The first Thursday</option> <option value="Friday">The first Friday</option> <option value="Saturday">The first Saturday</option> <option value="day">The first day</option> <option value="weekday">The first weekday</option> </select> </div> <div class="action-panel-control-wrap saved-search-weekly-additional"> <label for="saved-search-weekly-on-day" class="action-panel-label"> Which day? </label> <select id="saved-search-weekly-on-day" class="no-border-panel-selector saved-search-weekly-on-day"> <option value="Sunday">Sunday</option> <option value="Monday">Monday</option> <option value="Tuesday">Tuesday</option> <option value="Wednesday">Wednesday</option> <option value="Thursday">Thursday</option> <option value="Friday">Friday</option> <option value="Saturday">Saturday</option> </select> </div> <div class="action-panel-control-wrap"> <label for="saved-search-report" class="action-panel-label"> Report format: </label> <select id="saved-search-report" class="no-border-panel-selector saved-search-report"> <option value="DocSum">Summary</option> <option value="DocSumText">Summary (text)</option> <option value="Abstract">Abstract</option> <option value="AbstractText">Abstract (text)</option> <option value="MEDLINE">PubMed</option> </select> </div> <div class="action-panel-control-wrap"> <label for="saved-search-amount" class="action-panel-label"> Send at most: </label> <select id="saved-search-amount" class="no-border-panel-selector saved-search-amount"> <option value="1">1 item</option> <option value="5" selected>5 items</option> <option value="10">10 items</option> <option value="20">20 items</option> <option value="50">50 items</option> <option value="100">100 items</option> <option value="200">200 items</option> </select> </div> <div> <input type="checkbox" id="saved-search-send-if-no-result" class="saved-search-send-if-no-result" name="saved-search-send-if-no-result"> <label for="saved-search-send-if-no-result" class="action-panel-label smaller-checkbox"> Send even when there aren't any new results </label> </div> <div class="action-panel-control-wrap option-text-in-email-wrap"> <label for="saved-search-email-text" class="action-panel-label"> Optional text in email: </label> <textarea name="saved-search-email-text" id="saved-search-email-text" class="saved-search-email-text"></textarea> </div> </div> <div class="action-panel-actions"> <button class="action-panel-submit" type="submit" data-loading-label="Saving..." data-ga-category="save_share" data-ga-action="alert" data-ga-label="save"> Save </button> <button class="action-panel-cancel" aria-label="Close 'Your saved search' panel" ref="linksrc=close_saved_search_panel" aria-controls="saved-search-action-panel" aria-expanded="false" data-ga-category="save_share" data-ga-action="alert" data-ga-label="cancel"> Cancel </button> </div> </form> </div> </div> <div id="citation-manager-action-panel" class="citation-manager-action-panel action-panel" aria-hidden="true"> <div class="inner-wrap"> <h2 class="action-panel-heading"> Create a file for external citation management software </h2> <form id="citation-manager-action-panel-form" class="action-panel-content action-form" action="/results-export-ids/" data-by-search-action="/results-export-search-data/" data-by-ids-action="/results-export-ids/" method="post" data-by-search-method="post" data-by-ids-method="post"> <input type="hidden" name="csrfmiddlewaretoken" value="wPqrKgBMwpRKYBv3H1cVoAVmKocIKMxlv1gk1YKH16A1tT7xs7dz8IFE2Pj7iWXH"> <input name="results-format" type="hidden" value="pubmed"/> <div class="action-panel-actions"> <button class="action-panel-submit" type="submit" data-loading-label="Sending..." data-ga-category="save_share" data-ga-action="citation_manager" data-ga-label="save"> Create file </button> <button class="action-panel-cancel" aria-label="Close 'Send citations to citation manager' panel" ref="linksrc=close_citation_manager_panel" aria-controls="citation-manager-action-panel" aria-expanded="false" data-ga-category="save_share" data-ga-action="citation_manager" data-ga-label="cancel"> Cancel </button> </div> </form> </div> </div> <div id="rss-action-panel" class="rss-action-panel action-panel " aria-hidden="true"> <div class="inner-wrap"> <h2 class="action-panel-heading"> Your RSS Feed </h2> <form id="rss-action-panel-form" class="rss-action-panel-form action-panel-content action-form" data-create-rss-feed-url="/create-rss-feed-url/" data-search-form-term-value=""> <input type="hidden" name="csrfmiddlewaretoken" value="wPqrKgBMwpRKYBv3H1cVoAVmKocIKMxlv1gk1YKH16A1tT7xs7dz8IFE2Pj7iWXH"> <div class="action-panel-control-wrap"> <label for="rss-name" class="action-panel-label required-field-asterisk"> Name of RSS Feed: </label> <input maxlength="200" placeholder="Name" type="text" name="rss-name" id="rss-name" class="rss-name" value='' required pattern="[^"&=<>\/]*" title="The following characters are not allowed in the Name field: "&=<>/"> </div> <div class="rss-limit-wrap"> <div class="action-panel-control-wrap action-panel-extra-margin-top"> <label for="rss-limit" class="action-panel-label"> Number of items displayed: </label> <select id="rss-limit" class="no-border-panel-selector rss-limit"> <option value="5">5</option> <option value="10">10</option> <option value="15" selected="selected">15</option> <option value="20">20</option> <option value="50">50</option> <option value="100">100</option> </select> </div> </div> <div class="action-panel-actions"> <button class="action-panel-submit" type="submit" data-loading-label="Creating..." data-ga-category="save_share" data-ga-action="alert" data-ga-label="save"> Create RSS </button> <button class="action-panel-cancel" aria-label="Close 'Your RSS' panel" ref="linksrc=close_rss_panel" aria-controls="rss-action-panel" aria-expanded="false" data-ga-category="save_share" data-ga-action="alert" data-ga-label="cancel"> Cancel </button> </div> <div class="action-panel-control-wrap rss-link-copy-wrap"> <label for="rss-link" class="usa-sr-only">RSS Link</label> <input placeholder="Your RSS Feed Link" type="text" name="rss-link" id="rss-link" class="rss-link" title="RSS Link"> <button type="button" disabled class="rss-link-copy-button disabled" data-ga-category="save_share" data-ga-action="rss" data-ga-label="copy"> Copy </button> </div> </form> </div> </div> </div> </div> <div class="article-page" id="article-page" data-article-pmid="39021019"> <aside class="page-sidebar"> <div class="inner-wrap"> <div class="actions-buttons sidebar"><h3 class="title">Actions</h3><div class="inner-wrap"><button class="citation-button citation-dialog-trigger" aria-label="Open dialog with citation text in different styles" data-ga-category="save_share" data-ga-action="cite" data-ga-label="open" data-all-citations-url="/39021019/citations/" data-citation-style="nlm" data-pubmed-format-link="/39021019/export/"><span class="button-label">Cite</span></button><link type="text/css" href="ncbi-overlay-block/src/overlay-block.css"><div class="collections-button-container" data-article-id="39021019" data-article-db="pubmed"><button class="collections-button collections-dialog-trigger" aria-label="Save article in MyNCBI collections." data-ga-category="collections_button" data-ga-action="click" data-ga-label="collections_button" data-collections-open-dialog-enabled="false" data-collections-open-dialog-url="https://account.ncbi.nlm.nih.gov/?back_url=https%3A%2F%2Fpubmed.ncbi.nlm.nih.gov%2F39021019%2F%23open-collections-dialog" data-in-collections="false"><span class="button-label">Collections</span></button><div class="overlay" role="dialog"><div id="collections-action-dialog" class="dialog collections-dialog" aria-hidden="true"><div class="title">Add to Collections</div><div class="collections-action-panel action-panel"><form id="collections-action-dialog-form" class="collections-action-panel-form action-panel-content action-form action-panel-smaller-selectors" data-existing-collections-url="/list-existing-collections/" data-add-to-existing-collection-url="/add-to-existing-collection/" data-create-and-add-to-new-collection-url="/create-and-add-to-new-collection/" data-myncbi-max-collection-name-length="100" data-collections-root-url="https://www.ncbi.nlm.nih.gov/myncbi/collections/"><input type="hidden" name="csrfmiddlewaretoken" value="wPqrKgBMwpRKYBv3H1cVoAVmKocIKMxlv1gk1YKH16A1tT7xs7dz8IFE2Pj7iWXH"><div class="choice-group" role="radiogroup"><ul class="radio-group-items"><li><input type="radio" id="collections-action-dialog-new" class="collections-new" name="collections" value="new" data-ga-category="collections_button" data-ga-action="click" data-ga-label="collections_radio_new"><label for="collections-action-dialog-new">Create a new collection</label></li><li><input type="radio" id="collections-action-dialog-existing" class="collections-existing" name="collections" value="existing" checked="true" data-ga-category="collections_button" data-ga-action="click" data-ga-label="collections_radio_existing"><label for="collections-action-dialog-existing">Add to an existing collection</label></li></ul></div><div class="controls-wrapper"><div class="action-panel-control-wrap new-collections-controls"><label for="collections-action-dialog-add-to-new" class="action-panel-label required-field-asterisk"> Name your collection: </label><input type="text" name="add-to-new-collection" id="collections-action-dialog-add-to-new" class="collections-action-add-to-new" pattern="[^"&=<>\/]*" title="The following characters are not allowed in the Name field: "&=<>/" maxlength="100" data-ga-category="collections_button" data-ga-action="create_collection" data-ga-label="non_favorties_collection"><div class="collections-new-name-too-long usa-input-error-message selection-validation-message"> Name must be less than 100 characters </div></div><div class="action-panel-control-wrap existing-collections-controls"><label for="collections-action-dialog-add-to-existing" class="action-panel-label"> Choose a collection: </label><select id="collections-action-dialog-add-to-existing" class="action-panel-selector collections-action-add-to-existing" data-ga-category="collections_button" data-ga-action="select_collection" data-ga-label="($('.collections-action-add-to-existing').val() === 'Favorites') ? 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6009, Australia and International Space Centre, M468, University of Western Australia, Perth, Western Australia 6009, Australia." href="#full-view-affiliation-1" ref="linksrc=author_aff"> 1 </a></sup></span> </div> </div> </div> <div class="short-article-details"> Affiliations <button class="more-details" id="toggle-authors" data-alt-text="Collapse" aria-controls="expanded-authors" aria-expanded="false" data-pinger-ignore data-fetch-url="/39021019/long-authors/" data-id-prefix=""> <span class="title"> Expand </span> </button> </div> <div class="extended-article-details" id="expanded-authors" aria-hidden="true"> <div class="expanded-authors" id="full-view-expanded-authors"> <div class="affiliations"> <h3 class="title"> Affiliation </h3> <ul class="item-list"> <li data-affiliation-id="full-view-affiliation-1" id="full-view-affiliation-1" ><sup class="key">1</sup> <a href="https://ror.org/05sd1pp77">International Centre for Radio Astronomy Research</a>, M468, <a href="https://ror.org/047272k79">University of Western Australia</a>, Perth, Western Australia 6009, Australia and International Space Centre, M468, University of Western Australia, Perth, Western Australia 6009, Australia.</li> </ul> </div> </div> </div> <ul class="identifiers" id="full-view-identifiers"> <li> <span class="identifier pubmed"> <span class="id-label"> PMID: </span> <strong class="current-id" title="PubMed ID">39021019</strong> </span> </li> <li> <span class="identifier doi"> <span class="id-label"> DOI: </span> <a class="id-link" target="_blank" rel="noopener" ref="linksrc=article_id_link&article_id=10.1103/PhysRevE.109.065102&id_type=DOI" href="https://doi.org/10.1103/physreve.109.065102" data-ga-category="full_text" data-ga-action="DOI" > 10.1103/PhysRevE.109.065102 </a> </span> </li> </ul> <div class="in-clipboard-label " hidden> Item in Clipboard </div> </div> <div class="short-view" id="short-view-heading"> <h1 class="heading-title"> From cavitation to 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University of Western Australia, Perth, Western Australia 6009, Australia." href="#short-view-affiliation-1" ref="linksrc=author_aff"> 1 </a></sup></span> </div> </div> <div class="affiliations"> <h3 class="title"> Affiliation </h3> <ul class="item-list"> <li data-affiliation-id="short-view-affiliation-1" id="short-view-affiliation-1" ><sup class="key">1</sup> <a href="https://ror.org/05sd1pp77">International Centre for Radio Astronomy Research</a>, M468, <a href="https://ror.org/047272k79">University of Western Australia</a>, Perth, Western Australia 6009, Australia and International Space Centre, M468, University of Western Australia, Perth, Western Australia 6009, Australia.</li> </ul> </div> </div> <ul class="identifiers" id="short-view-identifiers"> <li> <span class="identifier pubmed"> <span class="id-label"> PMID: </span> <strong class="current-id" title="PubMed ID">39021019</strong> </span> </li> <li> <span class="identifier doi"> <span class="id-label"> DOI: </span> <a class="id-link" target="_blank" rel="noopener" ref="linksrc=article_id_link&article_id=10.1103/PhysRevE.109.065102&id_type=DOI" href="https://doi.org/10.1103/physreve.109.065102" data-ga-category="full_text" data-ga-action="DOI" > 10.1103/PhysRevE.109.065102 </a> </span> </li> </ul> <div class="in-clipboard-label " hidden> Item in Clipboard </div> </div> </div> </header> <div class="actions-buttons inline"><div class="inner-wrap"><button class="citation-button citation-dialog-trigger" aria-label="Open dialog with citation text in different styles" data-ga-category="save_share" data-ga-action="cite" data-ga-label="open" data-all-citations-url="/39021019/citations/" data-citation-style="nlm" data-pubmed-format-link="/39021019/export/"><span class="button-label">Cite</span></button><button class="more-actions-button more-actions-dialog-trigger" title="Open dialog with more actions to take" ref="linksrc=more_actions_btn"></button><div class="display-options" data-format-key="format" data-default-format-value="abstract" data-current-format-value="abstract" role="region"><button class="trigger usa-button" title="Change format" data-ga-category="display_options" data-ga-action="display_options_dialog"><span class="button-label">Display options</span></button><div class="dropdown" hidden><div class="title"> Display options </div><div class="content"><div class="format-container"><span class="option-label"> Format </span><select name="format" data-initial-value="abstract" aria-label="Display format" id="inline-actions-display-format"><option value="abstract">Abstract</option><option value="pubmed">PubMed</option><option value="pmid">PMID</option></select></div></div></div></div></div></div> <div class="abstract" id="abstract"> <h2 class="title"> Abstract </h2> <div class="abstract-content selected" id="eng-abstract"> <p> Differential equations of the form R[over ̈]=-kR^{γ}, with a positive constant k and real parameter γ, are fundamental in describing phenomena such as the spherical gravitational collapse (γ=-2), the implosion of cavitation bubbles (γ=-4), and the orbital decay in binary black holes (γ=-7). While explicit elemental solutions exist for select integer values of γ, more comprehensive solutions encompassing larger subsets of γ have been independently developed in hydrostatics (see Lane-Emden equation) and hydrodynamics (see Rayleigh-Plesset equation). I here present a universal explicit solution for all real γ, invoking the beta distribution. Although standard numerical ordinary differential equation solvers can readily evaluate more general second-order differential equations, this explicit solution reveals a hidden connection between collapse motions and probability theory that enables further analytical manipulations, it conceptually unifies distinct fields, and it offers insights into symmetry properties, thereby enhancing our understanding of these pervasive differential equations. </p> </div> </div> <p class="disclaimer" id="disclaimer"> <a href="/disclaimer/" target="_blank" data-ga-category="literature_resources" data-ga-action="disclaimer_link" data-ga-label="under_abstract">PubMed Disclaimer</a> </p> <div class="similar-articles" id="similar"> <h2 class="title"> Similar articles </h2> <ul class="articles-list" id="similar-articles-list"> <li class="full-docsum"> <div class="docsum-content" style="display:inline;"> <a class="docsum-title" href="/36714866/" ref="article_id=36714866&linksrc=similar_articles_link&ordinalpos=1" data-ga-category="similar_article" data-ga-action="36714866" data-ga-label=""> Cavitation in a soft porous material. </a> <div class="docsum-citation full-citation"> <span class="docsum-authors full-authors">Leng Y, Vlachos PP, Juanes R, Gomez H.</span> <span class="docsum-authors short-authors">Leng Y, et al.</span> <span class="docsum-journal-citation full-journal-citation">PNAS Nexus. 2022 Aug 18;1(4):pgac150. doi: 10.1093/pnasnexus/pgac150. eCollection 2022 Sep.</span> <span class="docsum-journal-citation short-journal-citation">PNAS Nexus. 2022.</span> <span class="citation-part">PMID: <span class="docsum-pmid">36714866</span></span> <span class="free-resources spaced-citation-item citation-part">Free PMC article.</span> </div> </div> </li> <li class="full-docsum"> <div class="docsum-content" style="display:inline;"> <a class="docsum-title" href="/33148086/" ref="article_id=33148086&linksrc=similar_articles_link&ordinalpos=2" data-ga-category="similar_article" data-ga-action="33148086" data-ga-label=""> A novel Chebyshev neural network approach for solving singular arbitrary order Lane-Emden equation arising in astrophysics. </a> <div class="docsum-citation full-citation"> <span class="docsum-authors full-authors">Mall S, Chakraverty S.</span> <span class="docsum-authors short-authors">Mall S, et al.</span> <span class="docsum-journal-citation full-journal-citation">Network. 2020 Feb-Nov;31(1-4):142-165. doi: 10.1080/0954898X.2020.1807636. 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