Efficient simulation of complex patterns in reaction-diffusion systems

Efficient numerical simulation techniques based on iterative and multigrid concepts are developed for solving coupled, nonlinear, reaction-diffusion systems. The solution approach is developed in a general setting and then applied to specific reaction-diffusion systems that give rise to complex dynamical patterns. The numerical strategy is based on semidiscretizing the coupled equations using a finite-difference formulation, with time integration of the resulting system of ordinary differential equations. Iterative and multigrid strategies are used to improve integration efficiency and to accelerate convergence. Numerical experiments are carried out to demonstrate the performance of the methods.