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A Class of Higher-Order Collocation Scheme for the Integral Equation of the Convolution Type

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  • M. Alsahlanee
  • P. Darania
  • S. Pishbin

Abstract

Auto convolution Volterra integral equations (ACVIEs) are the particular form of non-standard integral equations arising in mathematical modeling processes and the computation of certain functions. In this paper, a novel class of multistep collocation methods (NM-SCMs) is constructed in order to find a higher-order method is constructed for the numerical solution of this kind of the ACVIEs. We analyze the convergence of this method and determine the order of convergence. Also, 1-SCMs and M-SCMs are applied to solve this equation numerically.

Suggested Citation

  • M. Alsahlanee & P. Darania & S. Pishbin, 2025. "A Class of Higher-Order Collocation Scheme for the Integral Equation of the Convolution Type," Journal of Mathematics, Hindawi, vol. 2025, pages 1-15, February.
    • Handle: RePEc:hin:jjmath:8838147
    DOI: 10.1155/jom/8838147
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