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Superconvergent Galerkin method for second-order Fredholm–Volterra integro-differential equations

Author

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  • Agrawal, Shivam Kumar
  • Chakraborty, Samiran
  • Nelakanti, Gnaneshwar

Abstract

In this article, we approximate second-order nonlinear Fredholm–Volterra integro-differential equations (IDEs) with given boundary conditions. The Galerkin method based on the Kumar–Sloan technique is employed, utilizing piecewise polynomial basis functions. We achieve superconvergence rates without employing the traditional iterated Galerkin method available for integral equations and IDEs. Furthermore, we attain superconvergence results for the derivative of the approximate solution, which are identical to those for the approximation. Numerical experiments are provided to illustrate and validate the theory.

Suggested Citation

  • Agrawal, Shivam Kumar & Chakraborty, Samiran & Nelakanti, Gnaneshwar, 2026. "Superconvergent Galerkin method for second-order Fredholm–Volterra integro-differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 241(PA), pages 805-824.
    • Handle: RePEc:eee:matcom:v:241:y:2026:i:pa:p:805-824
    DOI: 10.1016/j.matcom.2025.10.004
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