Approximate Solutions for A Model of Reaction-Diffusion System with Slow Reaction and Fast Diffusion
In this paper, perturbation and finite difference methods are used to solve a reaction diffusion system. This system is modeled for describing the interaction between species in ecology. The interaction is interpreted as traveling wave solutions for both species under three types of initial conditions which describe some ecological cases. Types of traveling wave solutions are found and studied using numerical and approximate methods when there exists a small parameter appear in one of the equation. The solutions of the two methods are compared and show a good agreement.
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