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Superconvergent spectral methods for system of modified Volterra Integral Equations

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  • Kumar, Rakesh
  • Kant, Kapil
  • Rathish Kumar, B.V.

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.

Suggested Citation

  • Kumar, Rakesh & Kant, Kapil & Rathish Kumar, B.V., 2026. "Superconvergent spectral methods for system of modified Volterra Integral Equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 239(C), pages 115-134.
    • Handle: RePEc:eee:matcom:v:239:y:2026:i:c:p:115-134
    DOI: 10.1016/j.matcom.2025.05.011
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