Research On Numerical Methods For Reaction-Diffusion System

The di?erence method for parabolic equations is discussed in this paper,wherethere are many practical schemes ,design ideas, and their numerical stability-analyses.It is a reaction-di?usion type model for the population density of bacterialcells and the concentration of nutrient.The essential assumption is that thereexist two type of bacterial cells;active cells that move actively,grow and per-form cell division,and inactive ones that do nothing at all.Reaction-di?usion systems whose kinetics contain a stable limit cycle are anestablished class of models for a range of oscillatory biological and chemicalphenomena. In this paper,the author compares several numerical methodsfor calculating the solutions generated by spatially localized perturbationsfor one particular reaction-di?usion system.