Blow-Up Behavior of Collocation Solutions to Hammerstein-Type Volterra Integral Equations

Z. W. Yang, H. Brunner

Research output: Contribution to journalJournal articlepeer-review

11 Citations (Scopus)
21 Downloads (Pure)


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
Issue number4
Publication statusPublished - 1 Aug 2013

Scopus Subject Areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Adaptive stepsize
  • Collocation methods
  • Convergence of numerical blow-up time
  • Finite-time blow-up
  • Nonlinear Volterra integral equations


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