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

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. Therefo...

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Bibliographic Details
Published in:	AL-Rafidain journal of computer sciences and mathematics Vol. 9; no. 1; pp. 13 - 21
Main Authors:	Abbas Y. Al-Bayati, Saad Manaa, Abdulghafor M. Al-Rozbayani
Format:	Journal Article
Language:	English
Published:	Mosul University 01.07.2012
Subjects:	explicit runge kutta method finite difference methods gray-scott model in two dimensions implicit runge kutta method method of lines
ISSN:	1815-4816, 2311-7990
Online Access:	Get full text
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Summary:	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.
ISSN:	1815-4816 2311-7990
DOI:	10.33899/csmj.2012.163667