Scholarlink

<p>This paper investigates the design and analysis of numerical methods specifically tailored to highly oscillatory Volterra integral equations with Bessel kernels. First, we analyze the oscillatory behavior of the solution by leveraging the resolvent kernel and asymptotic properties of highly oscillatory integrals. Second, we employ the block collocation boundary value method and Filon quadrature rule to discretize the integral equations. Third, we conduct a convergence analysis with respect to the oscillation by examining the collocation error. Finally, we present several numerical examples to illustrate the effectiveness of the proposed methods.</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

Efficient block collocation methods for highly oscillatory Volterra integral equations with Bessel kernels

  • 期刊论文

  • 发表日期：

    2025年7月12日

查看全文
  • Chunping Ouyang,
  • Junjie Ma

摘要

This paper investigates the design and analysis of numerical methods specifically tailored to highly oscillatory Volterra integral equations with Bessel kernels. First, we analyze the oscillatory behavior of the solution by leveraging the resolvent kernel and asymptotic properties of highly oscillatory integrals. Second, we employ the block collocation boundary value method and Filon quadrature rule to discretize the integral equations. Third, we conduct a convergence analysis with respect to the oscillation by examining the collocation error. Finally, we present several numerical examples to illustrate the effectiveness of the proposed methods.