Efficient methods for Volterra integral equations with highly oscillatory Bessel kernels

Shuhuang Xiang*, Hermann BRUNNER

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

46 Citations (Scopus)


In this paper, we introduce efficient methods for the approximation of solutions to weakly singular Volterra integral equations of the second kind with highly oscillatory Bessel kernels. Based on the asymptotic analysis of the solution, we derive corresponding convergence rates in terms of the frequency for the Filon method, and for piecewise constant and linear collocation methods. We also present asymptotic schemes for large values of the frequency. These schemes possess the property that the numerical solutions become more accurate as the frequency increases.

Original languageEnglish
Pages (from-to)241-263
Number of pages23
JournalBIT Numerical Mathematics
Issue number1
Publication statusPublished - Mar 2013

Scopus Subject Areas

  • Software
  • Computer Networks and Communications
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Bessel function kernel
  • Highly oscillatory kernel
  • Volterra integral equation
  • Weak kernel singularity


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