The solution of the two-dimensional sine-Gordon equation using the method of lines

Authors:
A. G. Bratsos
Affiliations:
Department of Mathematics, Technological Educational Institution (T.E.I.) of Athens, 122 10 Egaleo, Athens, Greece
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 5
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A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions

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Abstract

The method of lines is used to transform the initial/boundary-value problem associated with the two-dimensional sine-Gordon equation in two space variables into a second-order initial-value problem. The finite-difference methods are developed by replacing the matrix-exponential term in a recurrence relation with rational approximants. The resulting finite-difference methods are analyzed for local truncation error, stability and convergence. To avoid solving the nonlinear system a predictor-corrector scheme using the explicit method as predictor and the implicit as corrector is applied. Numerical solutions for cases involving the most known from the bibliography line and ring solitons are given.