On spectral methods for Volterra integral equations and the convergence analysis

Tao TANG*, Xiang Xu, Jin Cheng

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

159 Citations (Scopus)

Abstract

The main purpose of this work is to provide a novel numerical approach for the Volterra integral equations based on a spectral approach. A Legendre-collocation method is proposed to solve the Volterra integral equations of the second kind. We provide a rigorous error analysis for the proposed method, which indicates that the numerical errors decay exponentially provided that the kernel function and the source function are sufficiently smooth. Numerical results confirm the theoretical prediction of the exponential rate of convergence. The result in this work seems to be the first successful spectral approach (with theoretical justification) for the Volterra type equations.

Original languageEnglish
Pages (from-to)825-837
Number of pages13
JournalJournal of Computational Mathematics
Volume26
Issue number6
Publication statusPublished - Nov 2008

Scopus Subject Areas

  • Computational Mathematics

User-Defined Keywords

  • Convergence analysis.
  • Legendre-spectral method
  • Second kind Volterra integral equations

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