ABSTRACT
This chapter considers general two-dimensional reaction-diffusion systems. Reaction-diffusion equations have been used successfully to model chemical and biological processes that involve pattern formations. Numerical solutions of such equations are important for computer simulation of patterns and data analysis. A. M. Turing first suggested in 1952 that some patterns that occur in chemistry are resulted from interaction between chemical reaction and diffusion. According to the reaction-diffusion theory, patterns are formed by the linear instability of the system and this instability eventually will be controlled by nonlinearity. Because of this nature of the problem, highly stable numerical methods are necessary for computer simulations of these patterns to ensure that patterns obtained by computer simulations are formed by the instability of the original system not by numerical instability.
