Numerical Solution and Stability Analysis of the Sine-Gordon Equation
The Sine – Gordon equation has been solved numerically by using two finite differences methods: The first is the explicit scheme and the second is the Crank – Nicholson scheme. A comparison between the two schemes has been made and the results were found to be : the first scheme is simpler and has f...
| Main Authors: | , |
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| Format: | Article |
| Language: | Arabic |
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Mosul University
2007-07-01
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| Series: | Al-Rafidain Journal of Computer Sciences and Mathematics |
| Subjects: | |
| Online Access: | https://csmj.mosuljournals.com/article_164002_4f2763aa77b4c29810dcede770b819b8.pdf |
| Summary: | The Sine – Gordon equation has been solved numerically by using two finite differences methods: The first is the explicit scheme and the second is the Crank – Nicholson scheme. A comparison between the two schemes has been made and the results were found to be : the first scheme is simpler and has faster convergence while the second scheme is more accurate . Also , the stability analysis of the two methods by the use of Fourier (Von Neumann) method has been done and the results were found to be : The explicit scheme is conditionally stable if and the Crank–Nicholson is unconditionally stable . |
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| ISSN: | 1815-4816 2311-7990 |