A note on Jacobi spectral-collocation methods for weakly singular Volterra integral equations with smooth solutions

Yanping Chen*, Xianjuan Li, Tao TANG

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

39 Citations (Scopus)

Abstract

This work is concerned with spectral Jacobi-collocation methods for Volterra integral equations of the second kind with a weakly singular of the form (t-s). When the underlying solutions are sufficiently smooth, the convergence analysis was carried out in [Chen & Tang, J. Comput. Appl. Math., 233 (2009), pp. 938-950]; due to technical reasons the results are restricted to 0 < μ < 1/2 In this work, we will improve the results to the general case 0 < μ < 1 and demonstrate that the numerical errors decay exponentially in the infinity and weighted norms when the smooth solution is involved.

Original languageEnglish
Pages (from-to)47-56
Number of pages10
JournalJournal of Computational Mathematics
Volume31
Issue number1
DOIs
Publication statusPublished - Jan 2013

Scopus Subject Areas

  • Computational Mathematics

User-Defined Keywords

  • Convergence analysis
  • Spectral-collocation methods
  • Volterra integral equations

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