The Finite Difference Methods for φ4 Klein-Gordon Equation
We solved φ<sup>4</sup> 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 i...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Mosul University
2008-12-01
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| Series: | Al-Rafidain Journal of Computer Sciences and Mathematics |
| Subjects: | |
| Online Access: | https://csmj.mosuljournals.com/article_163970_aea69361cfbd0a4e1027bf1100b2b9b4.pdf |
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| Summary: | We solved φ<sup>4</sup> 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. |
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| ISSN: | 1815-4816 2311-7990 |