@Article{cmes.2005.009.151,
AUTHOR = {Chein-Shan Liu, Yu-Ling Ku},
TITLE = {A Combination of Group Preserving Scheme and Runge-Kutta Method for the Integration of Landau-Lifshitz Equation},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {9},
YEAR = {2005},
NUMBER = {2},
PAGES = {151--178},
URL = {http://www.techscience.com/CMES/v9n2/24886},
ISSN = {1526-1506},
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.},
DOI = {10.3970/cmes.2005.009.151}
}