Finite difference scheme for the Landau-Lifshitz equation (Q692036)

The authors give a finite difference scheme for the Landau-Lifshitz equation. The Landau-Lifshitz equation is a nonlinear parabolic partial differential equation, and it is used to model the evolution of spin fields in continuum ferromagnetic material. The authors claim that the proposed scheme preserves the inherited properties of the Landau-Lifshitz equation such as length and energy conservation, etc. Stability and convergence of the proposed scheme are analyzed, and error estimation is also provided for the case with or without a termination condition, respectively.