| 二维波动方程的高精度交替方向隐式方法 |
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| 引用本文： | 马月珍,李小纲,葛永斌. 二维波动方程的高精度交替方向隐式方法[J]. 四川师范大学学报(自然科学版), 2010, 33(2). DOI: 10.3969/j.issn.1001-8395.2010.02.010 |
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| 作者姓名： | 马月珍 李小纲 葛永斌 |
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| 作者单位： | 宁夏大学,应用数学与力学研究所,宁夏,银川,750021 |
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| 摘 要： | 基于二阶微商的四阶紧致差商逼近公式及加权平均思想,提出了数值求解二维波动方程的2种精度分别为O(τ2+h4)和O(τ4+h4)的交替方向隐式(ADI)格式,以及与其相匹配的第一个时间层的同阶离散格式,并且通过Fourier方法分析了格式的稳定性.该方法在沿每个空间方向上只涉及3个网格基架点,因此可以重复采用TDMA算法,从而大大节省计算时间.数值实验验证了所用方法的精确性和可靠性.
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| 关 键 词： | 波动方程 高阶紧致格式 交替方向隐式方法 稳定性 |
A High-accuracy Alternating Direction Implicit Method for Solving the Two-dimensional Wave Equation |
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| MA Yue-zhen,LI Xiao-gang,GE Yong-bin. A High-accuracy Alternating Direction Implicit Method for Solving the Two-dimensional Wave Equation[J]. Journal of Sichuan Normal University(Natural Science), 2010, 33(2). DOI: 10.3969/j.issn.1001-8395.2010.02.010 |
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| Authors: | MA Yue-zhen LI Xiao-gang GE Yong-bin |
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| Affiliation: | MA Yue-zhen,LI Xiao-gang,GE Yong-bin(Institute of Applied Mathematics , Mechanics,Ningxia University,Yinchuan 750021,Ningxia) |
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| Abstract: | Based on the second- and fourth-order compact difference formulas for second-order derivatives and the idea of weighted average,two classes of the alternating direction implicit (ADI) method are proposed for solving two-dimensional wave equation.The methods are of accuracy O(τ~2+h~4) and O(τ~4+h~4) 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. |
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| Keywords: | wave equation high-order compact scheme alternating direction implicit method stability |
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