Zakharov方程Fourier谱方法的一致收敛性

数学物理学报 ›› 2013, Vol. 33 ›› Issue (3): 409-423.

Zakharov方程Fourier谱方法的一致收敛性

杨征^1,2|纪园园^1,3|马和平¹

1.上海大学数学系上海 200444|2.浙江丽水学院理学院 323000|3.上海财经大学经济学院上海 200433

收稿日期:2012-02-14 修回日期:2013-01-19 出版日期:2013-06-25 发布日期:2013-06-25
基金资助:
国家自然科学基金(11171209)、浙江省教育厅重点项目(z201120169)和上海市教委重点学科建设项目(J50101)资助.

Uniform Convergence of the Fourier Spectral Method for the Zakharov Equations

YANG Zheng^1,2, JI Yuan-Yuan^1,3, MA He-Ping¹

1.Department of Mathematics, Shanghai University, Shanghai 200444|2.College of Sciences, Lishui University, Zhejiang 323000|3.School of Economics, Shanghai University of Finance and Economics, Shanghai 200433

Received:2012-02-14 Revised:2013-01-19 Online:2013-06-25 Published:2013-06-25
Supported by:
国家自然科学基金(11171209)、浙江省教育厅重点项目(z201120169)和上海市教委重点学科建设项目(J50101)资助.

摘要/Abstract

摘要：

对Zakharov方程周期边值问题的Fourier谱方法给出了按H¹模的最优误差估计, 并获得了关于小参数ε的一致收敛性, 数值实验证实了理论分析结果. 文中还对一类相关方程的Fourier谱逼近设计了半隐时间离散格式, 稳定性好且便于实施. 最后, 通过与其他数值方法比较, 验证了该方法的有效性.

关键词: Zakharov方程, Fourier谱方法, 一致收敛性

Abstract:

In this paper, the optimal H¹ error estimate of the Fourier spectral method for the Zakharov equations with periodic boundary conditions is obtained and, especially, the uniform convergence with respect to the parameter ε is proved. Also, some semi-implicit time advancing scheme is proposed for the Fourier spectral approximation to a class of relative equations, which is of good stability and can be implemented efficiently.
At last, various numerical experiments are conducted to confirm the validity of the method.

Key words: Zakharov equations, Fourier spectral method, Uniform convergence

中图分类号:

65M12

杨征, 纪园园, 马和平. Zakharov方程Fourier谱方法的一致收敛性[J]. 数学物理学报, 2013, 33(3): 409-423.

YANG Zheng, JI Yuan-Yuan, MA He-Ping. Uniform Convergence of the Fourier Spectral Method for the Zakharov Equations[J]. Acta mathematica scientia,Series A, 2013, 33(3): 409-423.

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