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Volume 16, Issue 1
Multi-Symplectic Fourier Pseudospectral Method for the Kawahara Equation

Yuezheng Gong, Jiaxiang Cai & Yushun Wang

DOI: 10.4208/cicp.090313.041113a

Commun. Comput. Phys., 16 (2014), pp. 35-55.

Published online: 2014-07

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  • Abstract

In this paper, we derive a multi-symplectic Fourier pseudospectral scheme for the Kawahara equation with special attention to the relationship between the spectral differentiation matrix and discrete Fourier transform. The relationship is crucial for implementing the scheme efficiently. By using the relationship, we can apply the Fast Fourier transform to solve the Kawahara equation. The effectiveness of the proposed methods will be demonstrated by a number of numerical examples. The numerical results also confirm that the global energy and momentum are well preserved.

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COPYRIGHT: © Global Science Press

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@Article{CiCP-16-35, author = {Yuezheng Gong, Jiaxiang Cai and Yushun Wang}, title = {Multi-Symplectic Fourier Pseudospectral Method for the Kawahara Equation}, journal = {Communications in Computational Physics}, year = {2014}, volume = {16}, number = {1}, pages = {35--55}, abstract = {

In this paper, we derive a multi-symplectic Fourier pseudospectral scheme for the Kawahara equation with special attention to the relationship between the spectral differentiation matrix and discrete Fourier transform. The relationship is crucial for implementing the scheme efficiently. By using the relationship, we can apply the Fast Fourier transform to solve the Kawahara equation. The effectiveness of the proposed methods will be demonstrated by a number of numerical examples. The numerical results also confirm that the global energy and momentum are well preserved.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.090313.041113a}, url = {http://global-sci.org/intro/article_detail/cicp/7032.html} }
TY - JOUR T1 - Multi-Symplectic Fourier Pseudospectral Method for the Kawahara Equation AU - Yuezheng Gong, Jiaxiang Cai & Yushun Wang JO - Communications in Computational Physics VL - 1 SP - 35 EP - 55 PY - 2014 DA - 2014/07 SN - 16 DO - http://doi.org/10.4208/cicp.090313.041113a UR - https://global-sci.org/intro/article_detail/cicp/7032.html KW - AB -

In this paper, we derive a multi-symplectic Fourier pseudospectral scheme for the Kawahara equation with special attention to the relationship between the spectral differentiation matrix and discrete Fourier transform. The relationship is crucial for implementing the scheme efficiently. By using the relationship, we can apply the Fast Fourier transform to solve the Kawahara equation. The effectiveness of the proposed methods will be demonstrated by a number of numerical examples. The numerical results also confirm that the global energy and momentum are well preserved.

Yuezheng Gong, Jiaxiang Cai and Yushun Wang. (2014). Multi-Symplectic Fourier Pseudospectral Method for the Kawahara Equation. Communications in Computational Physics. 16 (1). 35-55. doi:10.4208/cicp.090313.041113a
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