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ARTICLE

A Combination of Group Preserving Scheme and Runge-Kutta Method for the Integration of Landau-Lifshitz Equation

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Computer Modeling in Engineering & Sciences 2005, 9(2), 151-178. https://doi.org/10.3970/cmes.2005.009.151

Abstract

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.

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