Finite difference scheme for the Landau-Lifshitz equation

Atsushi Fuwa, Tetsuya Ishiwata, Masayoshi Tsutsumi

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


In this paper we propose a finite difference scheme for the Landau-Lifshitz equation and the Heisenberg equation. These equations describe the evolution of spin fields in continuum ferromagnetism and have the following properties: (i) length preserving, (ii) energy conservation or dissipation property. We showthat our scheme inherits these characteristic properties. The proposed scheme is implicit nonlinear, so we check an unique solvability of our schemes. Furthermore, we establish the error estimate for this problem. Finally, we demonstrate numerical examples in order to show the effectiveness of our scheme.

Original languageEnglish
Pages (from-to)83-110
Number of pages28
JournalJapan Journal of Industrial and Applied Mathematics
Issue number1
Publication statusPublished - 2012 Feb


  • Error estimates
  • Finite difference scheme
  • Landau-Lifshitz equation

ASJC Scopus subject areas

  • General Engineering
  • Applied Mathematics


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