TY - JOUR
T1 - The Global Dufort-Frankel Difference Approximation for Nonlinear Reaction-Diffusion Equations
AU - Lu , Bainian
AU - Wan , Guohua
AU - Guo , Bolin
JO - Journal of Computational Mathematics
VL - 3
SP - 275
EP - 288
PY - 1998
DA - 1998/06
SN - 16
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/9159.html
KW - Globel Dufort-Frankel method, reaction-diffusion equation, global attractor, error estimate, numerical experiments.
AB - <p style="text-align: justify;">In this paper, the initial value problem of nonlinear reaction-diffusion equation is considered. The Dufort-Frankel finite difference approximation for the long time scheme is given for the $d$-dimensional reaction-diffusion equation with the two different cases. The global solution and global attractor are discussed for the Dufort-Frankel scheme. Moreover, properties of the solution are studied. The error estimate is presented in a finite time region and in the global time region for some special cases. Finally the numerical results for the equation are investigated for Allen-Cahn equation and some other equations and the homoclinic orbit is simulated numerically.</p>