@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 = {<p style="text-align: justify;">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.</p>},
issn = {2079-7338},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/nmtma/6015.html}
}