| 三维泊松方程基于Richardson外推法的高阶紧致差分方法 |
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| 引用本文： | 马月珍,葛永斌,王燕.三维泊松方程基于Richardson外推法的高阶紧致差分方法[J].数学的实践与认识,2011,41(8). |
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| 作者姓名： | 马月珍 葛永斌 王燕 |
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| 作者单位： | 1. 宁夏大学数学计算机学院,宁夏银川750021;宁夏同心县回民中学,宁夏同心751300
2. 宁夏大学数学计算机学院,宁夏银川,750021 |
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| 摘 要： | 基于Richardson外推法提出了数值求解三维泊松方程的高阶紧致差分方法.方法通过利用四阶和六阶紧致差分格式,分别在细网格和粗网格上求解,然后利用Richardson外推技术和算子插值方法,得到三维泊松方程在细网格上的六阶和八阶精度的数值解.数值实验结果验证了该方法的精确性和有效性.
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| 关 键 词： | 三维泊松方程 高阶紧致差分方法 Richardson外推法 交替方向隐式迭代 |
A High-Order Compact Difference Method Based on Richardson Extrapolation for the 3D Poisson Equation |
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| MA Yue-zhen,GE Yong-bin,WANG Yan.A High-Order Compact Difference Method Based on Richardson Extrapolation for the 3D Poisson Equation[J].Mathematics in Practice and Theory,2011,41(8). |
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| Authors: | MA Yue-zhen GE Yong-bin WANG Yan |
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| Institution: | MA Yue-zhen~(1,2),GE Yong-bin~1,WANG Yan~1 (1.College of Mathematics and Computer Science,Ningxia University,Yinchuan 750021,China) (2.Tongxin Hui Middle School,Tongxin 751300,China) |
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| Abstract: | A new high-order compact finite difference method based on the Richardson extrapolation technique is proposed to solve the three-dimensional Poisson equation.For a particular implementation,a fine grid equation and a coarse grid equation are solved by using a fourth-order and sixth-order compact difference scheme,then the Richardson extrapolation and an operator interpolation scheme are used by combining the two approximate solutions to get a sixth-order and eighth-order accuracy solution on fine grid.Numer... |
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| Keywords: | 3D poisson equation high order compact difference method Richardson extrapolation alternating direction implicit(ADI) iteration |
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