A Series Solution of the Cauchy Problem for Turing Reaction-diffusion Model

In this paper, the series pattern solution of the Cauchy problem for Turing reaction-diffusion model is obtained by using the homotopy analysis method (HAM). Turing reaction-diffusion model is nonlinear reaction-diffusion system which usually has power-law nonlinearities or may be rewritten in the form of power-law nonlinearities. Using the HAM, it is possible to find the exact solution or an approximate solution of the problem. This technique provides a series of functions which converges rapidly to the exact solution of the problem. The efficiency of the approach will be shown by applying the procedure on two problems. Furthermore, the so-called homotopy-Pade technique (HPT) is applied to enlarge the convergence region and rate of solution series given by the HAM.