 Superconvergent spectral methods for system of modified Volterra Integral EquationsRakesh Kumar, Kapil Kant and B.V. Rathish Kumar Mathematics and Computers in Simulation (MATCOM), 2026, vol. 239, issue C, 115-134 Abstract: This study introduces novel approaches, namely the Jacobi Spectral Galerkin (JSG) and Iterated Jacobi Spectral Galerkin (IJSG) techniques, designed specifically to solve a system of linear Volterra integral equations (SLVIEs). These equations involve mixed-type kernels, incorporating both weakly singular (WS) and smooth kernels simultaneously. Jacobi polynomial-based Galerkin and Iterated Galerkin (IG) techniques have been used to tackle these integral equations. Initially, the existence and uniqueness of solutions for both the Galerkin and IG methods are established. Later, the convergence analysis is carried out for smooth and non smooth solution cases. The major attraction of this paper is its exploration of non-smooth solutions, alongside achieving superconvergent results, distinguishing it from other articles. Improved convergence rates are achieved by the IJSG method over the JSG method. The theoretical results are numerically validated. Keywords: Volterra integral equation; Weakly singular kernel; Mixed type kernels; Galerkin method; Iterated Galerkin method (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:239:y:2026:i:c:p:115-134 DOI: 10.1016/j.matcom.2025.05.011 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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