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<p>In this article, we approximate nonlinear Fredholm–Hammerstein integro-differential equation with given initial conditions using Legendre polynomial-based Galerkin methods. Superconvergence results in the uniform norm are established for the approximate solution without relying on the traditional iterated Galerkin method. Moreover, enhanced superconvergence rates are achieved without employing the traditional iterated multi-Galerkin method. The same superconvergence rates in the uniform norm are also derived for the derivatives of the approximations in the proposed methods, without imposing any additional smoothness assumptions on the exact solution or the kernel involved. Theoretical results have been elucidated with numerical examples.</p>

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Superconvergent Legendre Galerkin methods for nonlinear Fredholm integro-differential equations

  • 期刊论文

  • 发表日期：

    2026年3月3日

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

摘要

In this article, we approximate nonlinear Fredholm–Hammerstein integro-differential equation with given initial conditions using Legendre polynomial-based Galerkin methods. Superconvergence results in the uniform norm are established for the approximate solution without relying on the traditional iterated Galerkin method. Moreover, enhanced superconvergence rates are achieved without employing the traditional iterated multi-Galerkin method. The same superconvergence rates in the uniform norm are also derived for the derivatives of the approximations in the proposed methods, without imposing any additional smoothness assumptions on the exact solution or the kernel involved. Theoretical results have been elucidated with numerical examples.