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<p>This paper is concerned with the numerical solution of third-kind Volterra integral equations with non-smooth kernels. Discontinuous Galerkin methods and two postprocessing techniques are introduced. First, the existence and uniqueness of the numerical solution are established. Then, the convergence of the numerical solutions and the global superconvergence of two postprocessed solutions are rigorously demonstrated in detail. Finally, some numerical results are given to confirm the theoretical predictions of convergence rates and superconvergence rates.</p>

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Discontinuous Galerkin Methods for Third-Kind Volterra Integral Equations with Non-smooth Kernels and Their Postprocessing Techniques

  • 期刊论文

  • 发表日期：

    2025年1月3日

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  • Zexiong Zhao,
  • Chengming Huang,
  • Zheng Ma

摘要

This paper is concerned with the numerical solution of third-kind Volterra integral equations with non-smooth kernels. Discontinuous Galerkin methods and two postprocessing techniques are introduced. First, the existence and uniqueness of the numerical solution are established. Then, the convergence of the numerical solutions and the global superconvergence of two postprocessed solutions are rigorously demonstrated in detail. Finally, some numerical results are given to confirm the theoretical predictions of convergence rates and superconvergence rates.