KdV方程的时间谱离散方法

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Spectral Method in Time for KdV Equations

Institute of Applied Mathematics, Academia Sinica, Laboratoryof Management Decison and Information Sysfems, AcademiaSinica, Beijing 100080, P. R. China

摘要: 本文提出了解KdV方程周期边值问题的安全港离散方法:在时间方向上采用Chebyshev拟谱逼近,在空间方向上采用Fourier Galerkin逼近。谱展开的系数由目标泛函的极小值来确定。同时证明了该方法的收敛性。
- KdV方程 /
- 谱方法 /
- Galerkin逼近 /
- 拟谱逼近
Abstract: This paper presents a fully spectral discretization method for solving KdV equations with periodic boundary conditions.Chebyshev pseudospectral approximation in the time direction and Fourier Galerkin approximation in the spatial direction.The expansion coefficients are determined by minimizing an object funictional.Rapid convergence of the method is proved.
- KdV equation /
- spectral method /
- Galerkin approximation /
- pseudospectral approximation

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