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Spectral approximated superconvergent methods for system of nonlinear Volterra Hammerstein integral equations

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

Abstract

In this article, we develop the Jacobi spectral multi-Galerkin method alongside the Kumar-Sloan technique to approximate systems of non-linear Volterra Hammerstein integral equations. We conduct a comprehensive superconvergence analysis for both smooth and weakly singular kernels in both infinity and weighted-L2 norms. Our findings include the derivation of superconvergence rates for the multi-Galerkin method without resorting to iterated versions. Notably, our conclusions highlight the enhanced performance of multi-Galerkin approximation compared to Jacobi spectral Galerkin methods, while maintaining the same system size for both Jacobi spectral multi-Galerkin and Galerkin methods. To validate the robustness and efficiency of our theoretical results, numerical examples are provided.

Suggested Citation

  • Chakraborty, Samiran & Agrawal, Shivam Kumar & Nelakanti, Gnaneshwar, 2025. "Spectral approximated superconvergent methods for system of nonlinear Volterra Hammerstein integral equations," Chaos, Solitons & Fractals, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:chsofr:v:192:y:2025:i:c:s0960077925000219
    DOI: 10.1016/j.chaos.2025.116008
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    References listed on IDEAS

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    1. Golbabai, A. & Keramati, B., 2008. "Easy computational approach to solution of system of linear Fredholm integral equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 568-574.
    2. Biazar, J. & Ghazvini, H., 2009. "He’s homotopy perturbation method for solving systems of Volterra integral equations of the second kind," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 770-777.
    3. Marzban, Hamid Reza & Nezami, Atiyeh, 2022. "Analysis of nonlinear fractional optimal control systems described by delay Volterra–Fredholm integral equations via a new spectral collocation method," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    4. Chakraborty, Samiran & Nelakanti, Gnaneshwar, 2023. "Superconvergence of system of Volterra integral equations by spectral approximation method," Applied Mathematics and Computation, Elsevier, vol. 441(C).
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