A Higher-Order Compact Finite Difference Method for Third-Order Boundary Value Problems with a Novel Treatment of Robin Boundary Conditions

A Higher-Order Compact Finite Difference Method for Third-Order Boundary Value Problems with a Novel Treatment of Robin Boundary Conditions | 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 A Higher-Order Compact Finite Difference Method for Third-Order Boundary Value Problems with a Novel Treatment of Robin Boundary Conditions Phumlani Dlamini Dlamini, Simphiwe Simelane This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9116317/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract This paper presents a higher-order compact finite difference method for solving third-order boundary value problems subject to Robin boundary conditions. The proposed scheme achieves sixth-order accuracy in the interior domain and incorporates a new boundary closure technique for Robin conditions to maintain this accuracy at the boundaries. A detailed error analysis is performed to establish the theoretical convergence properties of the method. Numerical experiments on several benchmark problems are conducted to validate the accuracy and efficiency of the scheme. The computed results confirm that the method attains the expected sixth-order rate of convergence and demonstrate its superiority over existing lower-order methods in terms of accuracy and computational efficiency. The proposed approach provides a reliable and effective tool for solving third-order boundary value problems subject to Robin boundary conditions. Compact finite differences third-order BVPs Robin boundary conditions Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 11 Apr, 2026 Reviews received at journal 10 Apr, 2026 Reviews received at journal 05 Apr, 2026 Reviewers agreed at journal 31 Mar, 2026 Reviewers agreed at journal 31 Mar, 2026 Reviewers invited by journal 31 Mar, 2026 Editor assigned by journal 30 Mar, 2026 Submission checks completed at journal 22 Mar, 2026 First submitted to journal 13 Mar, 2026 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. We do this by developing innovative software and high quality services for the global research community. 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