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Abstract <p>In this paper, we deal with a singularly perturbed neutral-type delay differential problem. To solve this problem numerically, we construct a novel difference scheme on a layer-adapted mesh with the finite difference method by using interpolated quadrature rules with remainder terms in integral form. We prove that this scheme is first-order uniformly convergent with respect to the small perturbation parameter in discrete maximum norm. We also present numerical experiments which confirm the theoretical findings.</p>

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A Uniform Numerical Method for Solving a Singularly Perturbed Neutral Delay Differential Equation

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • Y. Ekinci,
  • E. Cimen,
  • M. Cakir

摘要

Abstract

In this paper, we deal with a singularly perturbed neutral-type delay differential problem. To solve this problem numerically, we construct a novel difference scheme on a layer-adapted mesh with the finite difference method by using interpolated quadrature rules with remainder terms in integral form. We prove that this scheme is first-order uniformly convergent with respect to the small perturbation parameter in discrete maximum norm. We also present numerical experiments which confirm the theoretical findings.