| 泊松方程非等间距有限差分的数值求解方法 |
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| 引用本文： | 曹卫东,陆昌根,钱建华.泊松方程非等间距有限差分的数值求解方法[J].河海大学学报(自然科学版),2006,34(2):123-126. |
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| 作者姓名： | 曹卫东 陆昌根 钱建华 |
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| 作者单位： | 河海大学环境科学与工程学院,江苏,南京,210098 |
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| 摘 要： | 采用3阶精度中心差分格式对Dirichlet边界条件下的二维泊松方程进行离散,近边界网格点处采用2阶精度差分格式进行离散,利用超松弛迭代进行矩阵求解.数值计算结果表明,该有限差分方法具有收敛速度快、精度高的特点,可推广应用于非等间距网格下其他类型偏微分方程的数值求解.
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| 关 键 词： | 泊松方程 非等间距 差分格式 |
| 文章编号： | 1000-1980（2006）02-0123-04 |
| 收稿时间： | 2005-06-21 |
| 修稿时间： | 2005-06-21 |
Numerical solution of Poisson equation with non-uniform mesh finite difference scheme |
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| CAO Wei-dong,LU Chang-gen,QIAN Jian-hua.Numerical solution of Poisson equation with non-uniform mesh finite difference scheme[J].Journal of Hohai University (Natural Sciences ),2006,34(2):123-126. |
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| Authors: | CAO Wei-dong LU Chang-gen QIAN Jian-hua |
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| Institution: | College of Environmental Science and Engineering, Hohai University, Nanjing 210098, China |
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| Abstract: | The third-order accuracy center finite difference scheme was introduced to solve two-dimensional Poisson equations with Dirichlet boundary conditions, and the second-order accuracy finite difference scheme was applied to mesh discretization near boundaries.With the over-relaxation matrix iteration algorithm, the numerical solution was finally achieved.The present finite difference scheme is verified to be effective and accurate enough through case study,and it can be applied to solving other differential equations with non-uniform meshes. |
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| Keywords: | Poisson equation non-uniform difference scheme |
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