Supergeometric convergence of spectral collocation methods for weakly singular Volterra and fredholm integral equations with smooth solutions

Can Huang*, Tao TANG, Zhimin Zhang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)

Abstract

A spectral collocation method is proposed to solve Volterra or Predholm integral equations with weakly singular kernels and corresponding integro-differential equations by virtue of some identities. For a class of functions that satisfy certain regularity conditions on a bounded domain, we obtain geometric or supergeometric convergence rate for both types of equations. Numerical results confirm our theoretical analysis.

Original languageEnglish
Pages (from-to)698-719
Number of pages22
JournalJournal of Computational Mathematics
Volume29
Issue number6
DOIs
Publication statusPublished - Nov 2011

Scopus Subject Areas

  • Computational Mathematics

User-Defined Keywords

  • Collocation method
  • Integro-differential equations
  • Weakly singular kernel

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