Explicit- Implicit Runge-Kutta Methods to Solve the System of Nonlinear PPDEs in Two Dimensions | ||
| AL-Rafidain Journal of Computer Sciences and Mathematics | ||
| Article 1, Volume 9, Issue 1, June 2012, Pages 13-21 PDF (421.93 K) | ||
| Document Type: Research Paper | ||
| DOI: 10.33899/csmj.2012.163667 | ||
| Authors | ||
| Abbas Y. Al-Bayati1; Saad Manaa2; Abdulghafor M. Al-Rozbayani3 | ||
| 1College of Computer Sciences and Mathematics, University of Mosul, Iraq | ||
| 2Faculty of Science , University of Zakho, Iraq | ||
| 3Faculty of Science, University of Zakho, Iraq | ||
| 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. | ||
| Keywords | ||
| Gray-Scott model in two dimensions; Finite difference methods; Method of lines; Explicit Runge Kutta method; Implicit Runge Kutta method | ||
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