(untitled) (Journal of Computational Mathematics, 1997)
In this paper, a mean-field equation of motion which is derived by Penrose (1991) for the dynamic Ising model with Glauber dynamics is considered. Various finite difference schemes such as explicit Euler scheme, predictor-corrector scheme and some implicit schemes are given and their convergence, stabilities and dynamical properties are discussed. Moreover, a Lyapunov functional for the discrete semigroup { S}_n>0 is constructed. Finally, numerical examples are computed and analyzed. it shows that the model is a better approximation to Cahn-Allen equation which is mentioned in Penrose (1991).