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A numerical method for one-dimensional nonlinear sine-Gordon equation using multiquadric quasi-interpolation
Authors:Ma Li-Min and Wu Zong-Min
Institution:Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences, Fudan University, Shanghai 200433, China
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.
Keywords:quasi-interpolation  Hardy Multiquadric (MQ) interpolation methods  sine-Gordon equations  scattered data approximation  meshless method
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