Using the Landau-Lifshitz equation,the propagating of spin wave in metallic magnetic stripe has been investigated,in which the effective boundary condition is applied for the dynamic magnetization of the metallic magnetic strip.

We apply Lie group method and Cayley transformation to construct high order explicit square conserving scheme for the modulus conserving differential equations, such as the Euler equation, the Landau-Lifshitz equation and compare the numerical results with the classical Runge-Kutta method in modulus conserving and accuracy.

In this paper, the Landau-Lifshitz equation of ferromagentic chain systems is considered which is related to p-Laplacc operator, its solution from a m-dim compact manifold M(without hour dary) into the unit sphere S2 of R3 is shown; Sornc links between p --harmonicmaps and its solution are also established.

66Fe 5O12 with phase field method and worked out the Landau-Lifshitz-Gilbert equation by means of parallel method,fast Fourie transformation and Gauss-Sidel method in order to describe the process of magnetization.