A Crank-Nicolson scheme for the Landau-Lifshitz equation without damping
- Authors
- Jeong, Darae; Kim, Junseok
- Issue Date
- 15-5월-2010
- Publisher
- ELSEVIER SCIENCE BV
- Keywords
- Landau-Lifshitz equation; Crank-Nicolson; Finite difference method; Nonlinear multigrid method
- Citation
- JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, v.234, no.2, pp.613 - 623
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
- Volume
- 234
- Number
- 2
- Start Page
- 613
- End Page
- 623
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/116446
- DOI
- 10.1016/j.cam.2010.01.002
- ISSN
- 0377-0427
- Abstract
- 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. (C) 2010 Elsevier B.V. All rights reserved.
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