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The boundary integral equation approach for numerical solution of the one-dimensional sine-Gordon equation. (English) Zbl 1153.65099

Summary: 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.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
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