A numerical method for one-dimensional nonlinear sine-Gordon equation using multiquadric quasi-interpolation |
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Authors: | Ma Li-Min and Wu Zong-Min |
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Institution: | Shanghai Key Laboratory for Contemporary Applied
Mathematics, School of Mathematical Sciences,
Fudan University,
Shanghai 200433,
China |
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Abstract: | In this paper, we use a univariate multiquadric quasi-interpolation
scheme to solve the one-dimensional nonlinear sine-Gordon equation that
is related to many physical phenomena. We obtain a numerical scheme
by using the derivative of the quasi-interpolation to approximate
the spatial derivative and a difference scheme to approximate the
temporal derivative. The advantage of the obtained scheme is that
the algorithm is very simple so that it is very easy to implement.
The results of numerical experiments are presented and compared with
analytical solutions to confirm the good accuracy of the presented
scheme. |
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Keywords: | quasi-interpolation Hardy
Multiquadric (MQ) interpolation methods sine-Gordon equations scattered data approximation meshless method |
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