Analysis of collocation methods for nonlinear Volterra integral equations of the third kind

Huiming Song, Zhanwen Yang*, Hermann BRUNNER

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

We study the approximation of solutions of a class of nonlinear Volterra integral equations (VIEs) of the third kind by using collocation in certain piecewise polynomial spaces. If the underlying Volterra integral operator is not compact, the solvability of the collocation equations is generally guaranteed only if special (so-called modified graded) meshes are employed. It is then shown that for sufficiently regular data the collocation solutions converge to the analytical solution with the same optimal order as for VIEs with compact operators. Numerical examples are given to verify the theoretically predicted orders of convergence.

Original languageEnglish
Article number7
JournalCalcolo
Volume56
Issue number1
DOIs
Publication statusPublished - 1 Mar 2019

Scopus Subject Areas

  • Algebra and Number Theory
  • Computational Mathematics

User-Defined Keywords

  • Collocation methods
  • Convergence order
  • Noncompact Volterra integral operator
  • Nonlinear Volterra integral equations of the third kind
  • Solvability of collocation equations

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