A self-adaptive moving mesh method for the Camassa-Holm equation

Bao Feng Feng, Kenichi Maruno, Yasuhiro Ohta

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

A self-adaptive moving mesh method is proposed for the numerical simulations of the Camassa-Holm equation. It is an integrable scheme in the sense that it possesses the exact N-soliton solution. It is named a self-adaptive moving mesh method, because the non-uniform mesh is driven and adapted automatically by the solution. Once the non-uniform mesh is evolved, the solution is determined by solving a tridiagonal linear system. Due to these two superior features of the method, several test problems give very satisfactory results even if by using a small number of grid points.

Original languageEnglish
Pages (from-to)229-243
Number of pages15
JournalJournal of Computational and Applied Mathematics
Volume235
Issue number1
DOIs
Publication statusPublished - 2010 Nov 1
Externally publishedYes

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Keywords

  • Integrable semi-discretization
  • Peakon and cupson solutions
  • Self-adaptive moving mesh method
  • The Camassa-Holm equation

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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