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For the purpose of approximating the solution of second-kind Volterra integral equations with algebraic singularities at the diagonal and endpoints, this work explores a modified Nyström approach based on the zeros of the Jacobi polynomials. The technique employs the interpolating operator in suitable weighted spaces and the associated product integration formulae. The method is shown to be stable and more accurate than the standard Nyström scheme, and the precision of the solution can further be enhanced by using the Sloan iteration. The convergence and stability results are confirmed by several numerical experiments.

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Superconvergent Results for Solutions of Volterra Integral Equations with Weakly Singular Kernels in Weighted Spaces

  • 会议论文

  • 发表日期：

    2025年

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  • Abdelmajid El Bouayadi,
  • Chafik Allouch,
  • Ahmed Boujraf,
  • Mohamed Tahrichi

摘要

For the purpose of approximating the solution of second-kind Volterra integral equations with algebraic singularities at the diagonal and endpoints, this work explores a modified Nyström approach based on the zeros of the Jacobi polynomials. The technique employs the interpolating operator in suitable weighted spaces and the associated product integration formulae. The method is shown to be stable and more accurate than the standard Nyström scheme, and the precision of the solution can further be enhanced by using the Sloan iteration. The convergence and stability results are confirmed by several numerical experiments.