Spectral methods for weakly singular Volterra integral equations with smooth solutions

Yanping Chen*, Tao TANG

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

146 Citations (Scopus)


We propose and analyze a spectral Jacobi-collocation approximation for the linear Volterra integral equations (VIEs) of the second kind with weakly singular kernels. In this work, we consider the case when the underlying solutions of the VIEs are sufficiently smooth. In this case, we provide a rigorous error analysis for the proposed method, which shows that the numerical errors decay exponentially in the infinity norm and weighted Sobolev space norms. Numerical results are presented to confirm the theoretical prediction of the exponential rate of convergence. Crown

Original languageEnglish
Pages (from-to)938-950
Number of pages13
JournalJournal of Computational and Applied Mathematics
Issue number4
Publication statusPublished - 15 Dec 2009

Scopus Subject Areas

  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Error analysis
  • Smooth solutions
  • Spectral methods
  • Volterra integral equations
  • Weakly singular kernels


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