Spectral Method for Three-Dimensional Nonlinear Klein-Gordon Equation by Using Generalized Laguerre and Spherical Harmonic Functions

摘要

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.AMS subject classifications: 65M70, 41A30, 81Q05