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Volume 7, Issue 1
A Spectral Method for a Class of System of Multi-Dimensional Nonlinear Wave Equations

Xin-Min Xiang

J. Comp. Math., 7 (1989), pp. 41-55.

Published online: 1989-07

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  • Abstract

In [1,2], the problem of three-dimensional soliton of a class of system for three-dimensional nonlinear wave equations was investigated, and the existence and stability of three-dimensional soliton was proved. In [3] the system discusses in [1,2] was generalized and a more general class of system of multi-dimensional nonlinear wave equations were studied. It was proved that the solution of its initial-boundary value problem was well posed under some conditions. This system has been studied by the finite difference method and the finite element method [4,5]. In this paper, we take the trigonometric functions as a basis to derive a spectral method for the system and give a strict error analysis in theory.

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@Article{JCM-7-41, author = {Xin-Min Xiang}, title = {A Spectral Method for a Class of System of Multi-Dimensional Nonlinear Wave Equations}, journal = {Journal of Computational Mathematics}, year = {1989}, volume = {7}, number = {1}, pages = {41--55}, abstract = {

In [1,2], the problem of three-dimensional soliton of a class of system for three-dimensional nonlinear wave equations was investigated, and the existence and stability of three-dimensional soliton was proved. In [3] the system discusses in [1,2] was generalized and a more general class of system of multi-dimensional nonlinear wave equations were studied. It was proved that the solution of its initial-boundary value problem was well posed under some conditions. This system has been studied by the finite difference method and the finite element method [4,5]. In this paper, we take the trigonometric functions as a basis to derive a spectral method for the system and give a strict error analysis in theory.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9454.html} }
TY - JOUR T1 - A Spectral Method for a Class of System of Multi-Dimensional Nonlinear Wave Equations AU - Xin-Min Xiang JO - Journal of Computational Mathematics VL - 1 SP - 41 EP - 55 PY - 1989 DA - 1989/07 SN - 7 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9454.html KW - AB -

In [1,2], the problem of three-dimensional soliton of a class of system for three-dimensional nonlinear wave equations was investigated, and the existence and stability of three-dimensional soliton was proved. In [3] the system discusses in [1,2] was generalized and a more general class of system of multi-dimensional nonlinear wave equations were studied. It was proved that the solution of its initial-boundary value problem was well posed under some conditions. This system has been studied by the finite difference method and the finite element method [4,5]. In this paper, we take the trigonometric functions as a basis to derive a spectral method for the system and give a strict error analysis in theory.

Xin-Min Xiang. (1989). A Spectral Method for a Class of System of Multi-Dimensional Nonlinear Wave Equations. Journal of Computational Mathematics. 7 (1). 41-55. doi:
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