Finite difference scheme for the Landau-Lifshitz equation

被引：15

作者：

Fuwa, Atsushi ^{[2
]}

Ishiwata, Tetsuya ^{[1
]}

Tsutsumi, Masayoshi ^{[3
]}

机构：

[1] Shibaura Inst Technol, Saitama, Japan

[2] Mizuho Informat & Res Inst, Tokyo, Japan

[3] Waseda Univ, Tokyo, Japan

来源：

JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS | 2012年 / 29卷 / 01期

关键词：

Finite difference scheme; Error estimates; Landau-Lifshitz equation; FERROMAGNETISM; EXISTENCE;

D O I：

10.1007/s13160-011-0054-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 show that 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.

引用

页码：83 / 110

页数：28

共 15 条

[1] ON GLOBAL WEAK SOLUTIONS FOR LANDAU-LIFSHITZ EQUATIONS - EXISTENCE AND NONUNIQUENESS [J].