Numerical Approximation of the 3rd Order Pseudo-Parabolic Equation Using Collocation Technique

Numerical Approximation of the 3rd Order Pseudo-Parabolic Equation Using Collocation Technique | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Numerical Approximation of the 3 rd Order Pseudo-Parabolic Equation Using Collocation Technique Neeraj Dhiman, Mohammad Tamsir, Khaled A. Aldwoah, Mohammed A. Almalahi, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4966063/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 20 Nov, 2024 Read the published version in Boundary Value Problems → Version 1 posted 10 You are reading this latest preprint version Abstract This study aims to numerically approximate the solution of third-order pseudo-parabolic partial differential equations (PDEs), which exhibit both parabolic and hyperbolic characteristics. To achieve this, the cubic trigonometric tension B-spline collocation technique is employed for spatial discretization, while the finite difference method (FDM) is used for time discretization. The precision and consistency of the proposed numerical method are analyzed through the approximation of two illustrative examples, demonstrating its accuracy and reliability. A stability analysis, conducted using the von Neumann method, confirms that the method is unconditionally stable. The results show that the method effectively manages large-scale problems, with the numerical solution remaining bounded over time for the considered equations. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 20 Nov, 2024 Read the published version in Boundary Value Problems → Version 1 posted Editorial decision: Revision requested 04 Oct, 2024 Reviews received at journal 03 Oct, 2024 Reviews received at journal 29 Sep, 2024 Reviewers agreed at journal 06 Sep, 2024 Reviewers agreed at journal 01 Sep, 2024 Reviewers agreed at journal 30 Aug, 2024 Reviewers invited by journal 30 Aug, 2024 Editor assigned by journal 27 Aug, 2024 Submission checks completed at journal 26 Aug, 2024 First submitted to journal 23 Aug, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4966063","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":357057689,"identity":"3c2edbc1-a9a7-4ccd-82de-219dc84f3d82","order_by":0,"name":"Neeraj Dhiman","email":"","orcid":"","institution":"Graphic Era (deemed to be) University","correspondingAuthor":false,"prefix":"","firstName":"Neeraj","middleName":"","lastName":"Dhiman","suffix":""},{"id":357057692,"identity":"dd915c1c-3ac1-411e-af48-80115f7e5ef0","order_by":1,"name":"Mohammad Tamsir","email":"","orcid":"","institution":"Jazan University","correspondingAuthor":false,"prefix":"","firstName":"Mohammad","middleName":"","lastName":"Tamsir","suffix":""},{"id":357057693,"identity":"8ece0a65-a50c-4981-a544-de5ad92dc532","order_by":2,"name":"Khaled A. 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