TY  - EJOU
AU  - Ku, Chein-Shan Liu, Yu-Ling 

TI  - A Combination of Group Preserving Scheme and Runge-Kutta Method for the Integration of Landau-Lifshitz Equation
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2005
VL  - 9
IS  - 2
SN  - 1526-1506

AB  - In this paper we are concerned with the integration of a semi-discretized version of the Landau-Lifshitz equation, which is fundamental to describe the magnetization dynamics in micro/nano-scale magnetic systems. The resulting ordinary differential equations at the interior grid points are numerically integrated by a combination of the group preserving scheme derived by Liu (2004a) and the fourth-order Runge-Kutta method, abbreviated as GPS-RK4. The new method not only conserves the magnetization magnitude and has the fourth-order accuracy, but also preserves the Lyapunov property of the Landau-Lifshitz equation, namely the free energy is decreasing with time. In the limit of zero damping, the GPS-RK4 also well conserves the free energy constant in time. Numerical tests are performed to confirm the effectiveness of GPS-RK4.
KW  - Computational micromagnetics
KW  -  group preserving scheme
KW  -  Runge-Kutta method
KW  -  Landau-Lifshitz equation

DO  - 10.3970/cmes.2005.009.151