Numerical solutions of a time fractional reaction diffusion model for pattern formation in coral reefs

Abstract

In this paper, we propose a Time Fractional Reaction Diffusion mo del for the growth of corals in a tank and solve that model numerically. In order to do numerical simulations, we transformed the model equations in to a system of ordinary differential equations (ODEs} by discretising the model equations in space and repr esented it in a matrix form. Also, we represented the discrete Laplace operator of the model by a matrix embedding of the boundary conditions. We solved this system of ODEs using an explicit scheme, two implicit schemes and Matlab code FDE12 written by R. Garrappa which is an implementation of the predictor corrector method. We compared the solutions obtained by these numerical methods.