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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Vydáno v:	AL-Rafidain journal of computer sciences and mathematics Ročník 9; číslo 1; s. 13 - 21
Hlavní autoři:	Abbas Y. Al-Bayati, Saad Manaa, Abdulghafor M. Al-Rozbayani
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Mosul University 01.07.2012
Témata:	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
On-line přístup:	Získat plný text
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Popis
Shrnutí:	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