Approximate Solutions for a Couple of Reaction-diffusion Equations with Self-diffusion

In this paper, a competition model of a reaction diffusion system with self-diffusion has been studied using homotopy perturbation method, variational iteration method and Finite element method FEM (COMSOL package). The traveling wave solutions for this system are found and compared numerically.It was shown that the competition will lead at the end of the winning of one species. The effect of self diffusion is shown in the dispersing of traveling wave solution. Also, it was shown that the solution of finite element method and homotopy perturbation method are convergent to each other compared to the variation iteration method.