KdV方程的时间谱离散方法

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名

邮箱

手机号码

标题

留言内容

验证码

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

[1]	蒋伯诚等,《计算物理中的谱方法》,湖南科技出版社(1989).
[2]	G.Ierley,etc.,Spectral methods in time for a class of parabolic partial differential equations,J.Comp.Phys.,102(1992),88-97.
[3]	R.K.Dodd.Solitons and Nonlinear Wave Equations,Academic Press,London(1982).
[4]	王德人,《非线性方程组解法与最优化方沈》,人民教育出版社(1979).
[5]	R.G.Voigt,etc.,Spectral Method for PDE,SIAM Philadelpia(1984).
[6]	C.Canuto,etc.,Analysis of.the combinated finite element and Fourier interpolation,Numer.Math..39(1982).205-220.
[7]	李大潜等,《非线性发展方程》,科学出版社(1989),
[8]	P.Dutt,Spectral methods for initial boundary value problem-an alternative approach,SIAM J.Numer.Anal.,27,4(1990),885-903.
[9]	D.Gottlieb,Numerical analysis of spectral method,CBMS-NSF,Regional Conference Series in Applied Math.,26(1977)
[10]	R.A.Adams,Sobolev Spaces,Academia Press(1975)."