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.
| Original language | English |
|---|---|
| Pages (from-to) | 613-623 |
| Number of pages | 11 |
| Journal | Journal of Computational and Applied Mathematics |
| Volume | 234 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2010 May 15 |
Bibliographical note
Funding Information:This research was supported by the MKE (The Ministry of Knowledge Economy), Korea, under the ITRC (Information Technology Research Center) support program supervised by the NIPA (National IT Industry Promotion Agency) (NIPA-2009-C1090-0902-0013). This work was supported by National Research Foundation of Korea Grant funded by the Korean Government (2009-0074248).
Keywords
- Crank-Nicolson
- Finite difference method
- Landau-Lifshitz equation
- Nonlinear multigrid method
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics