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A non-linear prey-predator system solved numerically by Galerkin method, and we compare these results with the results of Pius Peter Nyaanga[6] who used finite difference methods, we found that Galerkin finite elements method is faster than finite difference method to reach equilibrium state where the density for the prey  and the predator  are equals for all the values for and , also we found that Galerkin method converges towards the steady state solutions faster than finite difference method with less steps in time.