A Multiscale Runge-Kutta Galerkin Method for One-dimensional sine-Gordon Equations
A Multiscale Runge-Kutta Galerkin Method for One-dimensional sine-Gordon Equations
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DOI：
10.12988/ams.2014.312692
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Jian Chen
中科院分区：
文献类型：
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作者：
Jian Chen
本文提出了求解Sine-Gordon方程的多尺度龙格-库塔Galerkin方法。基于文献[8]中构造的多尺度正交基的多尺度Galerkin方法用于离散空间变量，而经典的四阶显式RungeKutta方法用于求解所得到的非线性常微分方程组。由于多尺度基的强表示和Runge-Kutta方法的稳定性，在相对低维的子空间中得到了稳定和精确的近似解。所有的数值结果都说明了该算法的有效性。数学学科分类：65J15；65M60
In this paper the multiscale Runge-Kutta Galerkin method is presented for solving sine-Gordon equations. The multiscale Galerkin method based on the multiscale orthonormal bases constructed in [8] is used to discrete the spacial variable, and the classical four order explicit RungeKutta method is applied to solve the resulting nonlinear ordinary differential equations. Because of the strong expression of the multiscale bases and the stability of the Runge-Kutta method, stable and accurate approximate solutions are obtained in relatively low dimensional subspaces. All numerical results illustrate the effectiveness of the proposed algorithm. Mathematics Subject Classification: 65J15; 65M60