Scholarlink

<p>In this paper, a discontinuous Galerkin method is proposed to solve a singularly perturbed Volterra delay-integro-differential equation. First, the construction of a generalized Bakhvalov-type mesh and its corresponding properties are given. Furthermore, we prove an optimal parameter-uniform convergence rate <i>s</i> + 1 in the <i>L</i><sup>2</sup>-norm, where <i>s</i> is the degree of the piecewise polynomial space. Finally, a numerical experiment is carried out to confirm the theoretical results of our proposed numerical method.</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

Convergence analysis of a discontinuous Galerkin method on Bakhvalov-type meshes for a nonlinear singularly perturbed Volterra delay-integro-differential equation

  • 期刊论文

  • 发表日期：

    2026年8月5日

查看全文
  • Yige Liao,
  • Li-Bin Liu,
  • Xianbing Luo

摘要

In this paper, a discontinuous Galerkin method is proposed to solve a singularly perturbed Volterra delay-integro-differential equation. First, the construction of a generalized Bakhvalov-type mesh and its corresponding properties are given. Furthermore, we prove an optimal parameter-uniform convergence rate s + 1 in the L2-norm, where s is the degree of the piecewise polynomial space. Finally, a numerical experiment is carried out to confirm the theoretical results of our proposed numerical method.