A Compact Difference Scheme For A Class Of Nonlinear Reaction-Diffusion Equation With Variable Coefficient

Reaction-diffusion equation is widely applied in chemistry, biology and many other mathematical physics filed,and it has profound physical back-ground,so many boffins and engineer has been great interest in it. In this pa-per,it is mainly discuss in the numerical solution of a class of nonlinear reaction-diffusion equation with variable coefficient, and a compact finite difference is present .Existence and uniqueness of the difference solution are proved. It is also shown that the solution of compact difference scheme is convergent and unconditional stable in discrete norm L~∞and the convergence order O(h~4+τ~2).In addition, a numerical experiment illustrates the results of the presented method.This paper consists of five parts. In part one we mainly introduce the physical background of reaction-diffusion equations. In part two,we introduce the composition process of compact finite difference schemes. And in part three we analyse the compatibility,truncation error,stability of the compact finite difference. In part four,we give numerical experiments to the schemes. In part five, we give the compact finite difference schemes for a nonlinear reaction-diffusion system.