NUMERICAL ANALYSIS FOR A MEAN-FIELD EQUATION FOR THE ISING MODEL WITH GLAUBER DYNAMICS  

作　　者：Lu, BN Wan, GH 

机构地区：[1]SHAANXI NORMAL UNIV,DEPT MATH,XIAN,PEOPLES R CHINA

出　　处：《Journal of Computational Mathematics》1997年第3期203-218,共16页计算数学（英文）

摘　　要：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).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).

关 键 词：FIGURE NUMERICAL ANALYSIS FOR A MEAN-FIELD EQUATION FOR THE ISING MODEL WITH GLAUBER DYNAMICS MATH 

分 类 号：O241[理学—计算数学]