Finite difference scheme for two-dimensional periodic nonlinear Schrödinger equations

Younghun Hong, Chulkwang Kwak, Shohei Nakamura, Changhun Yang

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

A nonlinear Schrödinger equation (NLS) on a periodic box can be discretized as a discrete nonlinear Schrödinger equation (DNLS) on a periodic cubic lattice, which is a system of finitely many ordinary differential equations. We show that in two spatial dimensions, solutions to the DNLS converge strongly in L2 to those of the NLS as the grid size h> 0 approaches zero. As a result, the effectiveness of the finite difference method (FDM) is justified for the two-dimensional periodic NLS.

Original languageEnglish
Pages (from-to)391-418
Number of pages28
JournalJournal of Evolution Equations
Volume21
Issue number1
DOIs
StatePublished - Mar 2021

Bibliographical note

Publisher Copyright:
© 2020, Springer Nature Switzerland AG.

Keywords

  • Continuum limit
  • Periodic nonlinear Schrödinger equation
  • Uniform Strichartz estimate

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