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

作　　者：Xiao-Yong Zhang Ben-Yu Guo Yu-Jian Jiao 

机构地区：[1]Department of Mathematics, Shanghai Maritime University, PudongRoad, 1550, Shanghai, 200135, China. [2]Department of Mathematics, Shanghai Normal University, Scientific Computing Key Laboratory of Shanghai Universities, Division of Computational Science of E-institute of Shanghai Universities, Guilin Road 100, Shanghai, 200234, China.

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2009年第1期43-64,共22页高等学校计算数学学报（英文版）

基　　金：supported in part by NSF of China N.10871131;The Science and Technology Commission of Shanghai Municipality,Grant N.075105118;Shanghai Leading Academic Discipline Project N.T0401;Fund for E-institute of Shanghai Universities N.E03004.

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.In this paper, a generalized Laguerre-spherical harmonic spectral method is proposed for the Cauchy problem of three-dimensional nonlinear Klein-Gordon equa- tion. 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 es- tablish 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.

关 键 词：Generalized Laguerre-spherical harmonic spectral method Cauchy problem of nonlinear Klein-Gordon equation. 

分 类 号：O174.3[理学—数学] TS941.714[理学—基础数学]