Nonpolynomial Spline Collocation for Volterra Equations With Weakly Singular Kernels

Hermann BRUNNER*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

77 Citations (Scopus)

Abstract

Volterra integral equations of the second kind with weakly singular kernels possess, in general, solutions which are not smooth near the left endpoint of the interval of integration. Since ordinary polynomial spline collocation cannot lead to high-order convergence we introduce special nonpolymial spline spaces which are modelled after the structure of these solutions near the point of nonsmooth behavior; collocation in these spaces will once more lead to high-order methods. Analogous results are derived for Volterra integro-differential equations with weakly singular kernels.

Original languageEnglish
Pages (from-to)1106-1119
Number of pages14
JournalSIAM Journal on Numerical Analysis
Volume20
Issue number6
DOIs
Publication statusPublished - 1983

Scopus Subject Areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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