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 - <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>