Numerical Methods For A Class Of Reaction-Diffusion Equation

Reaction-Diffusion equations is widely applied in chemistry ,biologyand many other mathematical physics fields ,and it has profound physicalbackground, so many bo?ns and engineers has been great interest in it.both theory and numerical analysis need get deep research. In this paper itis mainly discuss in the numerical solution of a class of nonlinear reaction-di?usion equation, according to the feature and nature of this equation, wegive two different difference schemes. On processing of disperse, we use asuccessive linearization method for the item of nonlinear by its structure. Inthe paper we also has been minutely introduced the composition process ofdifference schemes, analysis the truncation error, on discussing of the schemestability, we use the energy approach to obtain the two different differencemethod stability condition. At last, comparing with formerly methods thesetwo schemes is more easily to calculate, and its stability conditions are betterthan other. According to compare two new difference schemes , they has thesame convergence precision, but the stability condition of Di?erence schemeTwo is better than Di?erence scheme One .In this work it consists of three parts, in part one we mainly intro-duce the physical background of Reaction-Diffusion equations and the exis-tence, unicity and regularity of solution, Meanwhile we introduce the resultof Reaction-Diffusion equations at the present stage. in part two, we hasminutely introduced the composition process of difference schemes, analysisthe compatibility , truncation error, stability, astringency and give numericalexperiments to the schemes ,we get the numerical solution and exact solution,through the graphic we get from the numerical experiment, we can explana-tion the stability, astringency intuitively. In the last part, we summarize theresult previously and put forward some new questions.