| THE GLOBAL DUFORT-FRANKEL DIFFERENCE APPROXIMATION FOR NONLINEAR REACTION-DIFFUSION EQUATIONS |
| |
| 作者单位： | Bai-nian Lu (Institute of Computational and Applied Mathematics，Xiangtan University，Xiangtan，411105，China; Laboratory of Computational Physics，Institute of Applied Physics and Computational Mathematics，Beijing 100088，China |
| |
| 摘 要： | 1.IntroductionInthispaperweconsiderthefollowinginitial-valueproblemofnonlinearreactiondiffusionequation:HerefiisaboundeddomaininRd(d<3)withaLipschitzboundaryOffand7isapositiveconstallt.Lettheset{in*l:j(u*)=0}benotemptyandu=ma-c{lu*I:f(u*)=0}.Assumptionont…
|
THE GLOBAL DUFORT-FRANKEL DIFFERENCE APPROXIMATION FOR NONLINEAR REACTION-DIFFUSION EQUATIONS |
| |
| Authors: | Bai-nian Lu |
| |
| Abstract: | 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 Alien-Cahn equation and some other equations and the homoclinic orbit is simulated numerically. |
| |
| Keywords: | globel Dufort-Frankel method reaction-diffusion eqution global attractor error estimate numerical experiments |
| 本文献已被 CNKI 等数据库收录！ |
