The finite difference method is considered for.the following initial-boundary- Value problem: where j(s), (x) and (x) are given functions; QT = [0, 1]× [0, T]. The convergence of the finite difference schemes is verified by discrete functional analysis methods and prior estimation techniques.
In this paper, the Landau-Lifshitz equation with periodic initial boundary val- ued problem which is govnered by ■μ／■ｔ=-α1μ×（μ×Δμ）+α2（μ×Δμ） is discreted by using the Euler-forword finite difference method. The proposed scheme is explicit so that the parallel algorithm can be used to simulate numerically on computer. Moreove, the convergence and stability of the proposed scheme are proved by the finite extensive method of the nonlinear function. Finally, the numerical experiments are provided to check the theoritical results.
