A numerical method for one-dimensional nonlinear sine-Gordon equation using multiquadric quasi-interpolation
A numerical method for one-dimensional nonlinear sine-Gordon equation using multiquadric quasi-interpolation
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DOI：
10.1088/1674-1056/18/8/001
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发表时间：
2009-08
影响因子：
1.7
通讯作者：
Ma Li-Min;Wu Zong-min
中科院分区：
文献类型：
--
作者：
Ma Li-Min;Wu Zong-min
在本文中，我们使用单变量多重二次准插值方案来求解与许多物理现象相关的一维非线性正弦戈登方程。我们通过使用准插值的导数来近似空间导数来获得数值格式，并使用差分格式来近似时间导数。所得到的方案的优点是算法非常简单，非常容易实现。给出了数值实验的结果，并与解析解进行了比较，以证实所提出方案的良好准确性。
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 difierence 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 conflrm the good accuracy of the presented scheme.