Zakharov方程Fourier谱方法的一致收敛性

Acta mathematica scientia,Series A ›› 2013, Vol. 33 ›› Issue (3): 409-423.

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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.

Abstract

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

CLC Number:

65M12

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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Uniform Convergence of the Fourier Spectral Method for the Zakharov Equations

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