{"paper_id":"009ec0c1-2c66-4608-890b-5f5b430217ef","body_text":"A novel super-convergent numerical method for solving nonlinear Volterra integral equations based on B-splines | 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 novel super-convergent numerical method for solving nonlinear Volterra integral equations based on B-splines Mohammad Ghasemi, Arash Goligerdian, Sina Moradi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3409913/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 25 May, 2024 Read the published version in Mediterranean Journal of Mathematics → Version 1 posted You are reading this latest preprint version Abstract ‎We introduce and thoroughly examine a novel approach grounded in B-spline techniques to address the solution of second-kind nonlinear Volterra integral equations‎. ‎Our method revolves around the application of B-spline interpolation‎, ‎incorporating innovative end conditions‎, ‎and delving into the associated existence and error estimation aspects‎. ‎Notably‎, ‎we develop this technique separately for even and odd-degree splines‎, ‎leading to super-convergent approximations‎, ‎particularly significant when employing even-degree splines‎. ‎This paper extends its commitment to a comprehensive analysis‎, ‎delving deeply into the method's convergence characteristics and providing insightful error bounds‎. ‎To empirically validate our approach‎, ‎we present a series of numerical experiments‎. ‎These experiments underscore the method's efficacy and practicality‎, ‎showcasing numerical approximations that closely align with the anticipated theoretical outcomes‎. ‎Our proposed method thus emerges as a promising and robust tool for addressing the challenging realm of nonlinear Volterra integral equations‎, ‎bridging the gap between theoretical expectations and practical applications‎. 2010 Mathematics Subject Classifications: 45Dxx; 65R20; 41A15. B-spline Volterra integral equations Super-convergence Gauss-Legendre quadrature Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 25 May, 2024 Read the published version in Mediterranean Journal of Mathematics → Version 1 posted 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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