Blow-up of finite-difference solutions to nonlinear wave equations

Norikazu Saito, Takiko Sasaki

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

Finite-difference schemes for computing blow-up solutions of one dimensional nonlinear wave equations are presented. By applying time increments control technique, we can introduce a numerical blow-up time which is an approximation of the exact blowup time of the nonlinear wave equation.After having verified the convergence of our proposed schemes, we prove that solutions of those finite-difference schemes actually blow up in the corresponding numerical blow-up times.Then, we prove that the numerical blow-up time converges to the exact blow-up time as the discretization parameters tend to zero.Several numerical examples that confirm the validity of our theoretical results are also offered.

Original languageEnglish
Pages (from-to)349-380
Number of pages32
JournalJournal of Mathematical Sciences (Japan)
Volume23
Issue number1
Publication statusPublished - 2016
Externally publishedYes

Keywords

  • Blow-up
  • Finite-difference method
  • Nonlinear wave equation

ASJC Scopus subject areas

  • Mathematics(all)

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