Scholarlink

<p>The purpose of this study is to solve a first-order singularly perturbed Fredholm integro-differential equation with a discontinuous source term by introducing the upwind difference scheme in conjunction with a composite trapezoidal rule on Shishkin mesh. Uniform first-order convergence is reliably achieved with respect to the perturbation parameter. Error estimates are derived in the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2627_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="26" /> </InlineMediaObject> <EquationSource Format="TEX">\(L_{\infty}\)</EquationSource> </InlineEquation> norm. To accelerate the rate of convergence we implement the Richardson extrapolation technique. Numerical experiments are performed to verify the accuracy of the theoretical estimates.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Parameter uniform numerical scheme for singularly perturbed fredholm integro-differential equation with an interior layer

  • 期刊论文

  • 发表日期：

    2025年8月25日

查看全文
  • Deepak Kumar,
  • S. Gowrisankar

摘要

The purpose of this study is to solve a first-order singularly perturbed Fredholm integro-differential equation with a discontinuous source term by introducing the upwind difference scheme in conjunction with a composite trapezoidal rule on Shishkin mesh. Uniform first-order convergence is reliably achieved with respect to the perturbation parameter. Error estimates are derived in the \(L_{\infty}\) norm. To accelerate the rate of convergence we implement the Richardson extrapolation technique. Numerical experiments are performed to verify the accuracy of the theoretical estimates.