| 三维热传导方程的紧交替方向差分格式 |
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| 引用本文： | 王晓峰,李订芳,李博,温成峰. 三维热传导方程的紧交替方向差分格式[J]. 数学杂志, 2010, 30(5) |
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| 作者姓名： | 王晓峰 李订芳 李博 温成峰 |
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| 作者单位： | 武汉大学数学与统计学院,湖北,武汉,430072 |
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| 基金项目： | Supported by NNSF of China(10971159) |
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| 摘 要： | 本文研究了三维热传导方程的紧交替方向隐式差分格式.利用算子方法导出了紧交替方向隐式差分格式,并利用Fourier分析方法证明了差分格式的收敛性和绝对稳定性,Richardson外推法外推一次得到具有O(T3+h6)阶精度的近似解.本文方法是对二维热传导方程问题的推广,同样适用于多维的情形.
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| 关 键 词： | 热传导方程 差分算子 紧交替方向差分格式 绝对稳定 |
COMPACT ADI METHOD FOR SOLVING HEAT EQUATIONS IN THREE-DIMENSION |
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| WANG Xiao-feng,LI Ding-fang,LI Bo,WEN Cheng-feng. COMPACT ADI METHOD FOR SOLVING HEAT EQUATIONS IN THREE-DIMENSION[J]. Journal of Mathematics, 2010, 30(5) |
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| Authors: | WANG Xiao-feng LI Ding-fang LI Bo WEN Cheng-feng |
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| Affiliation: | WANG Xiao-feng,LI Ding-fang,LI Bo,WEN Cheng-feng(School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China) |
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| Abstract: | An efficient high order compact alternating direction implicit (ADI) method is developed for solving three-dimensional heat equations by introducing some differential operators.It is shown by the discrete Fourier analysis that this new ADI scheme is unconditionally stable and the truncation error O(T-3 + h6) is also gained with once Richardson's extrapolation. The method can be generalized to the multi-dimensional case. |
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| Keywords: | heat equations differential operators ADI difference scheme unconditionally stable |
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