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13 ExplicitImplicit Runge-Kutta Methods to Solve the System of Nonlinear PPDEs in Two Dimensions Abbas Y. Al-Bayati Saad A. Manaa Abdulghafor M. Al-Rozbayani abdulghafor_rozbayani@uomosul.edu.iq 1,2 College of Computer Sciences and Mathematics, University of Mosul, Iraq Faculty of Science , University of Zakho, Iraq Received on: 11/06/2007 Accepted on: 15/08/2007 ABSTRACT In this paper, we will find the numerical solution of Gray-Scott model in two dimensions space, this method is a system of non-linear parabolic partial differential equations. Then transforming the original model (system of non-linear PPDEs), by using the method of lines to a system of ODEs. Therefore we used Runge-Kutta methods (Explicit RK method and Implicit RK method) to find the numerical solutions of the new systems, and we compared between these methods, we saw that the numerical results of IRK methods is more accurate than the numerical results of ERK method.

Explicit- Implicit Runge-Kutta Methods to Solve the System of Nonlinear PPDEs in Two Dimensions