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Volume 2, Issue 1
Spectral Method for Three-Dimensional Nonlinear Klein-Gordon Equation by Using Generalized Laguerre and Spherical Harmonic Functions

Xiao-Yong Zhang, Ben-Yu Guo & Yu-Jian Jiao

Numer. Math. Theor. Meth. Appl., 2 (2009), pp. 43-64.

Published online: 2009-02

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  • Abstract

In this paper, a generalized Laguerre-spherical harmonic spectral method is proposed for the Cauchy problem of three-dimensional nonlinear Klein-Gordon equation. The goal is to make the numerical solutions to preserve the same conservation as that for the exact solution. The stability and convergence of the proposed scheme are proved. Numerical results demonstrate the efficiency of this approach. We also establish some basic results on the generalized Laguerre-spherical harmonic orthogonal approximation, which play an important role in spectral methods for various problems defined on the whole space and unbounded domains with spherical geometry.

  • Keywords

Generalized Laguerre-spherical harmonic spectral method, Cauchy problem of nonlinear Klein-Gordon equation.

  • AMS Subject Headings

65M70, 41A30, 81Q05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-2-43, author = {Xiao-Yong Zhang, Ben-Yu Guo and Yu-Jian Jiao}, title = {Spectral Method for Three-Dimensional Nonlinear Klein-Gordon Equation by Using Generalized Laguerre and Spherical Harmonic Functions}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2009}, volume = {2}, number = {1}, pages = {43--64}, abstract = {

In this paper, a generalized Laguerre-spherical harmonic spectral method is proposed for the Cauchy problem of three-dimensional nonlinear Klein-Gordon equation. The goal is to make the numerical solutions to preserve the same conservation as that for the exact solution. The stability and convergence of the proposed scheme are proved. Numerical results demonstrate the efficiency of this approach. We also establish some basic results on the generalized Laguerre-spherical harmonic orthogonal approximation, which play an important role in spectral methods for various problems defined on the whole space and unbounded domains with spherical geometry.

}, issn = {2079-7338}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/nmtma/6015.html} }
TY - JOUR T1 - Spectral Method for Three-Dimensional Nonlinear Klein-Gordon Equation by Using Generalized Laguerre and Spherical Harmonic Functions AU - Xiao-Yong Zhang, Ben-Yu Guo & Yu-Jian Jiao JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 43 EP - 64 PY - 2009 DA - 2009/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/nmtma/6015.html KW - Generalized Laguerre-spherical harmonic spectral method, Cauchy problem of nonlinear Klein-Gordon equation. AB -

In this paper, a generalized Laguerre-spherical harmonic spectral method is proposed for the Cauchy problem of three-dimensional nonlinear Klein-Gordon equation. The goal is to make the numerical solutions to preserve the same conservation as that for the exact solution. The stability and convergence of the proposed scheme are proved. Numerical results demonstrate the efficiency of this approach. We also establish some basic results on the generalized Laguerre-spherical harmonic orthogonal approximation, which play an important role in spectral methods for various problems defined on the whole space and unbounded domains with spherical geometry.

Xiao-Yong Zhang, Ben-Yu Guo and Yu-Jian Jiao. (2009). Spectral Method for Three-Dimensional Nonlinear Klein-Gordon Equation by Using Generalized Laguerre and Spherical Harmonic Functions. Numerical Mathematics: Theory, Methods and Applications. 2 (1). 43-64. doi:
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