三维波动方程的高精度交替方向隐式方法  

A High-order Alternating Direction Implicit Method for Solving Three-dimensional Wave Equation

作　　者：马月珍[1] 田娣[1] 葛永斌[1] 

机构地区：[1]宁夏大学应用数学与力学研究所,宁夏银川750021

出　　处：《河南科技大学学报（自然科学版）》2008年第6期86-89,92,共5页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学基金项目(10502026;10662006)

摘　　要：提出了数值求解三维波动方程的2种精度分别为O(τ2+h4)和O(τ4+h4)的交替方向隐式(ADI)格式,并且通过Fourier方法证明了格式的稳定性。该方法在沿每个空间方向上只涉及三个网格基架点,因此可以重复采用TDMA算法,从而可以大大节省计算时间,数值实验验证了本文方法的精确性和可靠性。Two classes of the alternating direction implicit (ADI) method are proposed for solving three-dimensional wave equation.The methods are of order O(τ2+h4) and O(τ4+h4) respectively.Stability conditions are obtained by Fourier analysis method.For only three points are used on every time level,it permits to use TDMA algorithm with a considerable save of computing time.Numerical experiments prove the efficiency and dependability.

关 键 词：波动方程 高阶紧致格式 交替方向隐式方法 稳定性 

分 类 号：O241.82[理学—计算数学]