Convergence analysis of spectral Galerkin methods for Volterra type integral equations

Ziqing Xie, Xianjuan Li, Tao TANG*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

57 Citations (Scopus)

Abstract

This work is to provide spectral and pseudo-spectral Jacobi-Galerkin approaches for the second kind Volterra integral equation. The Gauss-Legendre quadrature formula is used to approximate the integral operator and the inner product based on the Jacobi weight is implemented in the weak formulation in the numerical implementation. For some spectral and pseudo-spectral Jacobi-Galerkin methods, a rigorous error analysis in both the infinity and weighted norms is given provided that both the kernel function and the source function are sufficiently smooth. Numerical experiments validate the theoretical prediction.

Original languageEnglish
Pages (from-to)414-434
Number of pages21
JournalJournal of Scientific Computing
Volume53
Issue number2
DOIs
Publication statusPublished - Nov 2012

Scopus Subject Areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Pseudo-spectral Galerkin
  • Spectral convergence
  • Spectral Galerkin
  • The second kind Volterra integral equations

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