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Numerical Solution and Stability Analysis of the Sine-Gordon Equation | ||
| AL-Rafidain Journal of Computer Sciences and Mathematics | ||
| Article 11, Volume 4, Issue 1, 2007, Pages 39-56 PDF (462.97 K) | ||
| Document Type: Research Paper | ||
| DOI: 10.33899/csmj.2007.164002 | ||
| Authors | ||
| Saad Abdullah Manna; Norjan Hasan Juma | ||
| College of Computer Science and Mathematics University of Mosul, Iraq | ||
| Abstract | ||
| 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 . | ||
| Keywords | ||
| Stability Analysis; Finite Differences Methods; Explicit Scheme; Crank – Nicholson method; Fourier (Von Neumann) method; Sine-Gordon Equation | ||
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