Finite difference approximation for nonlinear Schrödinger equations with application to blow-up computation

Norikazu Saito, Takiko Sasaki

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

This paper presents a coherent analysis of the finite difference method to nonlinear Schrödinger (NLS) equations in one spatial dimension. We use the discrete H1 framework to establish well-posedness and error estimates in the L norm. The nonlinearity f(u) of a NLS equation is assumed to satisfy only a growth condition. We apply our results to computation of blow-up solutions for a NLS equation with the nonlinearity f(u) = -

Original languageEnglish
Pages (from-to)427-470
Number of pages44
JournalJapan Journal of Industrial and Applied Mathematics
Volume33
Issue number2
DOIs
Publication statusPublished - 2016 Jul 1

Keywords

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

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics

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