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The Finite Difference Methods for φ4 Klein-Gordon Equation | ||
| AL-Rafidain Journal of Computer Sciences and Mathematics | ||
| Article 4, Volume 5, Issue 2, 2008, Pages 47-63 PDF (450.84 K) | ||
| Document Type: Research Paper | ||
| DOI: 10.33899/csmj.2008.163970 | ||
| Authors | ||
| Saad A. Manaa1; Laya Y. Hawell2 | ||
| 1College of Computer Sciences and Mathematics University of Mosul | ||
| 2College of Education University of Duhok | ||
| Abstract | ||
| We solved φ4 Klein-Gordon equation numerically by using two finite difference methods: The first is the explicit method and the second is the implicit (Crank-Nicholson) method. Also, we studied the numerical stability of the two methods using Fourier (Von Neumann) method and it has been found that the first method is simpler and has faster convergence while the second method is more accurate, and the explicit method is conditionally stable while the implicit method is unconditionally stable. | ||
| Keywords | ||
| Klein-Gordon equation; Finite difference methods; explicit method; implicit (Crank-Nicholson) method; numerical stability; Fourier (Von Neumann) method; Convergence | ||
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