Numerical solutions of reaction-diffusion systems with coupled diffusion terms

Numerical solutions of some initial-boundary value problem associated with a particular reaction-diffusion systems namely Gray-Scott model responsible for spatial pattern formation are considered. The aim of this paper is to numerically solve the above system with coupled diffusion terms. Firstly, using some linear transformations, a general form of diffusion coupled reactiondiffusion system is converted into reaction-diffusion system with uncoupled diffusion terms and then, some finite difference schemes (based on (Hoff 1978)) are constructed to obtain the solutions. Finally, the graphical representation of the numerical solutions are presented.