A Crank-Nicolson scheme for the Landau-Lifshitz equation without damping

Darae Jeong, Junseok Kim

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


An accurate and efficient numerical approach, based on a finite difference method with Crank-Nicolson time stepping, is proposed for the Landau-Lifshitz equation without damping. The phenomenological Landau-Lifshitz equation describes the dynamics of ferromagnetism. The Crank-Nicolson method is very popular in the numerical schemes for parabolic equations since it is second-order accurate in time. Although widely used, the method does not always produce accurate results when it is applied to the Landau-Lifshitz equation. The objective of this article is to enumerate the problems and then to propose an accurate and robust numerical solution algorithm. A discrete scheme and a numerical solution algorithm for the Landau-Lifshitz equation are described. A nonlinear multigrid method is used for handling the nonlinearities of the resulting discrete system of equations at each time step. We show numerically that the proposed scheme has a second-order convergence in space and time.

Original languageEnglish
Pages (from-to)613-623
Number of pages11
JournalJournal of Computational and Applied Mathematics
Issue number2
Publication statusPublished - 2010 May 15


  • Crank-Nicolson
  • Finite difference method
  • Landau-Lifshitz equation
  • Nonlinear multigrid method

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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