基于Associated Hermite正交基函数求解波动方程的算法研究  

A NEW METHOD FOR SOLVING WAVE PROBLEMS BASED ON THE ASSOCIATED HERMITE ORTHOGONAL FUNCTIONS

作　　者：盛俊 缪小平 Sheng Jun;Miao Xiaoping(Graduate School,The Army Engineering University of PLA,Nanjing 210007)

机构地区：[1]陆军工程大学研究生院,南京210007

出　　处：《高等学校计算数学学报》2018年第3期263-274,共12页Numerical Mathematics A Journal of Chinese Universities

摘　　要：波动方程是由麦克斯韦方程组导出的一种重要的偏微分方程，在声学、电磁学和流体力学等领域都有着十分广阔的应用，但波动方程的精确解一般很难求出，因此对其数值解法的研究就具有重要的实际意义．波动方程的数值解法主要包括有限差分法（Finite Difference Method，FDM）、有限元法、谱方法等．The stability conditions for solving the traditional finite difference method in solving the wave equation when the limit and the problem of low calculation efficiency, this paper proposes a AH （Associated Hermite） orthogonal basis function and the finite difference method （Finite Difference Method, FDM） - numerical algorithm combining-AH-FDM algorithm. In this algorithm, the wave equation is expanded by Hermite polynomial, and the time derivatives is eliminated by Galerkin method, and the unconditional convergence of the difference scheme is realized. Numerical examples show that, compared with the traditional finite difference method and the alternating direction implicit difference method, the proposed algorithm breaks the stability conditions and has higher efficiency while maintaining high accuracy.

关 键 词：波动方程 HERMITE 正交基函数 麦克斯韦方程组 算法 求解 数值解法 偏微分方程 

分 类 号：O241.82[理学—计算数学]