Convergence analysis of Jacobi spectral collocation methods for Abel-Volterra integral equations of second kind

Xianjuan Li, Tao TANG*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

50 Citations (Scopus)

Abstract

This work is to analyze a spectral Jacobi-collocation approximation for Volterra integral equations with singular kernel φ(t, s) = (t - s) . In an earlier work of Y. Chen and T. Tang [J. Comput. Appl. Math., 2009, 233: 938-950], the error analysis for this approach is carried out for 0 <μ<1/2 under the assumption that the underlying solution is smooth. It is noted that there is a technical problem to extend the result to the case of Abel-type, i. e., μ = 1/2. In this work, we will not only extend the convergence analysis by Chen and Tang to the Abel-type but also establish the error estimates under a more general regularity assumption on the exact solution.

Original languageEnglish
Pages (from-to)69-84
Number of pages16
JournalFrontiers of Mathematics in China
Volume7
Issue number1
DOIs
Publication statusPublished - Feb 2012

Scopus Subject Areas

  • Mathematics (miscellaneous)

User-Defined Keywords

  • Abel-Volterra integral equation
  • convergence analysis
  • Jacobi spectral collocation method

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