中国物理B ›› 2009, Vol. 18 ›› Issue (8): 3099-3103.doi: 10.1088/1674-1056/18/8/001

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A numerical method for one-dimensional nonlinear sine-Gordon equation using multiquadric quasi-interpolation

马利敏, 吴宗敏   

  1. Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences, Fudan University, Shanghai 200433, China
  • 收稿日期:2008-11-11 修回日期:2008-12-02 出版日期:2009-08-20 发布日期:2009-08-20
  • 基金资助:
    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).

A numerical method for one-dimensional nonlinear sine-Gordon equation using multiquadric quasi-interpolation

Ma Li-Min(马利敏)† and Wu Zong-Min(吴宗敏)   

  1. Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences, Fudan University, Shanghai 200433, China
  • Received:2008-11-11 Revised:2008-12-02 Online:2009-08-20 Published:2009-08-20
  • Supported by:
    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).

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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.

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.

Key words: quasi-interpolation, Hardy Multiquadric (MQ) interpolation methods, sine-Gordon equations, scattered data approximation, meshless method

中图分类号:  (Solitons)

  • 05.45.Yv
02.60.Ed (Interpolation; curve fitting) 02.60.Lj (Ordinary and partial differential equations; boundary value problems)