波动方程的高精度数值解方法  

High Accuracy Numerical Solution of Wave Equation

作　　者：袁洪旺 王希胤 李金 YUAN Hongwang;WANG Xiyin;LI Jin(Department of Mathematics,College of Science,North China University of Science and Technology,Tangshan,Hebei 063200,China;School of Science,North China University of Science and Technology,Tangshan,Hebei 063200,China)

机构地区：[1]华北理工大学理学院数学系,河北唐山063200 [2]华北理工大学理学院,河北唐山063200

出　　处：《计算物理》2024年第4期426-439,共14页Chinese Journal of Computational Physics

基　　金：国家自然科学基金(11771398);河北省自然科学基金(A2019209533)资助项目。

摘　　要：本文提出重心Lagrange插值配点法求解(2+1)维波动方程和(3+1)维波动方程。介绍了重心Lagrange插值法并且给出配点法的矩阵格式。波动方程的解函数和初边值条件均用Lagrange插值近似,利用配点法得到离散方程,获得波动方程的矩阵表达式。分别用附加法和置换法施加波动方程的初边值条件。数值算例表明:重心Lagrange插值配点法求解波动方程具有较高的计算精度和计算效率。A barycentric Lagrange interpolation collocation method is proposed to solve the three-dimensional and four-dimensional wave equations.Firstly,the barycentric Lagrange interpolation method is introduced and the matrix format of the collocation method is given.Secondly,the solution function and initial boundary conditions of the wave equation are approximated by Lagrange interpolation.The discrete equation is obtained by collocation method,and the matrix expression of the wave equation is obtained.Finally,the initial and boundary conditions of the wave equation are imposed by the addition method and the replacement method respectively.Numerical examples show that the barycentric Lagrange interpolation collocation method has high computational accuracy and efficiency.

关 键 词：重心Lagrange插值 波动方程 配点法 矩阵格式 

分 类 号：O469[理学—凝聚态物理]