TY - JOUR
T1 - Numerical Analysis for a Mean-Field Equation for the Ising Model with Glauber Dynamics
JO - Journal of Computational Mathematics
VL - 3
SP - 203
EP - 218
PY - 1997
DA - 1997/06
SN - 15
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/9200.html
KW - 
AB - <p style="text-align: justify;">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 $\{ S\}_{n&gt;0}$ 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).</p>