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TITLE 
ABSTRACT A reactiondiffusion system (RDS) as a mutualism model in ecology is studied using finite difference method and asymptotic methods. For non linear reaction term an explicit method is used and an implicit method for linear diffusion term. The numerical solutions are found as traveling wave solutions with no flux Neuman boundary conditions and for three different types of initial conditions which represent a common ecological cases. The asymptotic solutions are studied for this model when a small perturbed parameter ?«1 appear from non dimensional of (RDS). The traveling wave solutions from the above two methods are compared and shown a good agreement. 
KEYWORDS Reaction diffusion system, Mutualism, Finite difference methods, Asymptotic methods 
REFERENCES [1] AlyKhan K. and Lioyd N. T., Fourthorder timestepping for stiff PDEs, SIAM J Sci. Computer Vol.26, 2005, pp.1214–1233. [1] AlyKhan K. and Lioyd N. T., Fourthorder timestepping for stiff PDEs, SIAM J Sci. Computer Vol.26, 2005, pp.1214–1233. 
Cite this paper Shaker M. Rasheed, Faraj Omar. (2016) A Comparison Between Finite Difference and Asymptotic Methods for Solving a ReactionDiffusion Model in Ecology. International Journal of Mathematical and Computational Methods, 1, 393399 
