Blow-up behavior of collocation solutions to Hammerstein-type volterra integral equations

Z.W. Yang, Hermann Brunner

Research output: Contribution to journalArticle

6 Citations (Scopus)
122 Downloads (Pure)

Abstract

We analyze the blow-up behavior of one-parameter collocation solutions for Hammerstein-type Volterra integral equations (VIEs) whose solutions may blow up in finite time. To approximate such solutions (and the corresponding blow-up time), we will introduce an adaptive stepsize strategy that guarantees the existence of collocation solutions whose blow-up behavior is the same as the one for the exact solution. Based on the local convergence of the collocation methods for VIEs, we present the convergence analysis for the numerical blow-up time. Numerical experiments illustrate the analysis.



Original languageEnglish
Pages (from-to)2260-2282
Number of pages23
JournalSIAM Journal on Numerical Analysis
Volume51
Issue number4
DOIs
Publication statusPublished - 1 Aug 2013

Keywords

  • nonlinear Volterra integral equations
  • finite-time blow-up
  • collocation methods
  • adaptive stepsize
  • convergence of numerical blow-up time

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