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.
Received: 11 November 2008
Revised: 02 December 2008
Accepted manuscript online:
(Ordinary and partial differential equations; boundary value problems)
Fund: Project
supported by the State Key Development Program for Basic Research of
China (Grant No 2006CB303102), and Science and Technology Commission
of Shanghai Municipality, China (Grant No
09DZ2272900).
Cite this article:
Ma Li-Min(马利敏) and Wu Zong-Min(吴宗敏) A numerical method for one-dimensional nonlinear sine-Gordon equation using multiquadric quasi-interpolation 2009 Chin. Phys. B 18 3099
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