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<p>In this paper, an adaptive grid algorithm for solving a singularly perturbed Fredholm integral-differential equation with discontinuous coefficients is investigated. An upwind finite-difference scheme is established under an arbitrary nonuniform mesh, and an a posteriori error estimation is performed. Based on the a posteriori error estimation and equidistributed monitor function, an adaptive grid generation algorithm is constructed. Finally, numerical experiments verify that the algorithm is first-order uniformly convergent.</p>

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An Adaptive Grid Method for a Singularly Perturbed Fredholm Integro-Differential Equation with Discontinuous Coefficients

  • 期刊论文

  • 发表日期：

    2025年11月3日

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  • Ying Liang,
  • Li-Bin Liu,
  • Ciwen Zhu

摘要

In this paper, an adaptive grid algorithm for solving a singularly perturbed Fredholm integral-differential equation with discontinuous coefficients is investigated. An upwind finite-difference scheme is established under an arbitrary nonuniform mesh, and an a posteriori error estimation is performed. Based on the a posteriori error estimation and equidistributed monitor function, an adaptive grid generation algorithm is constructed. Finally, numerical experiments verify that the algorithm is first-order uniformly convergent.