@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} }