Numerical blow-up of semilinear parabolic PDEs on unbounded domains in R2

Jiwei Zhang, Houde Han, Hermann BRUNNER*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)

Abstract

We study the numerical solution of semilinear parabolic PDEs on unbounded spatial domains ω in R2 whose solutions blow up in finite time. Of particular interest are the cases where ω = R2 or ω is a sectorial domain in R2. We derive the nonlinear absorbing boundary conditions for corresponding, suitably chosen computational domains and then employ a simple adaptive time-stepping scheme to compute the solution of the resulting system of semilinear ODEs. The theoretical results are illustrated by a broad range of numerical examples.

Original languageEnglish
Pages (from-to)367-382
Number of pages16
JournalJournal of Scientific Computing
Volume49
Issue number3
DOIs
Publication statusPublished - Dec 2011

Scopus Subject Areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Adaptive time-stepping
  • Finite difference spatial discretization
  • Finite-time blow-up
  • Local nonlinear boundary conditions
  • Sectorial domains
  • Semilinear PDEs
  • Unbounded spatial domains

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