The boundary integral equation approach for numerical solution of the one‐dimensional Sine‐Gordon equation |
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| Authors: | Mehdi Dehghan Davoud Mirzaei |
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| Affiliation: | Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran 15914, Iran |
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| Abstract: | This article describes a numerical method based on the boundary integral equation and dual reciprocity method for solving the one‐dimensional Sine‐Gordon (SG) equation. The time derivative is approximated by the time‐stepping method and a predictor–corrector scheme is employed to deal with the nonlinearity which appears in the problem. Numerical results are presented for some problems to demonstrate the usefulness and accuracy of this approach. In addition, the conservation of energy in SG equation is investigated. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008 |
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| Keywords: | boundary integral equation dual reciprocity method Sine‐Gordon equation conservation of energy |
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