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A numerical method for one-dimensional nonlinear sine-Gordon equation using multiquadric quasi-interpolation 被引量:5

A numerical method for one-dimensional nonlinear sine-Gordon equation using multiquadric quasi-interpolation
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摘要 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. 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.
出处 《Chinese Physics B》 SCIE EI CAS CSCD 2009年第8期3099-3103,共5页 中国物理B(英文版)
基金 supported by the State Key Development Program for Basic Research of China (Grant No 2006CB303102) Science and Technology Commission of Shanghai Municipality,China (Grant No 09DZ2272900)
关键词 QUASI-INTERPOLATION Hardy Multiquadric (MQ) interpolation methods sine-Gordon equations scattered data approximation meshless method quasi-interpolation, Hardy Multiquadric (MQ) interpolation methods, sine-Gordon equations, scattered data approximation, meshless method
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