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The Finite Difference Methods for Hyperbolic – Parabolic Equations | ||
| AL-Rafidain Journal of Computer Sciences and Mathematics | ||
| Article 7, Volume 2, Issue 2, 2005, Pages 57-71 PDF (405.17 K) | ||
| Document Type: Research Paper | ||
| DOI: 10.33899/csmj.2005.164084 | ||
| Authors | ||
| Abbas Y. Al-Bayati1; Saad A. Manaa2; Ekhlass S. Al-Rawi1 | ||
| 1College of Computer Sciences and Mathematics University of Mosul, Mosul, Iraq | ||
| 2College of Computer Sciences and Mathematics University of Mosul/Iraq | ||
| Abstract | ||
| The objective of this paper is to construct numerical schemes using finite difference methods for the one-dimensional general hyperbolic- parabolic- reaction problem. The finite difference method with the exponential transformation form is used to solve the problem, and employs difference approximation technique to obtain the numerical solutions. Computational examples are presented and compared with the exact solutions. We obtained that the Crank-Nicholson scheme is more accurate than Forward scheme. Therefore the form of exponential transformation for the problem yields a stable solution compared with exact solution. | ||
| Keywords | ||
| Finite difference methods; Exponential transformation; Crank-Nicholson scheme; Hyperbolic- parabolic- reaction problem | ||
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