| 含两个小参数的抛物对流扩散方程的有限差分法 |
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| 引用本文： | 岑仲迪.含两个小参数的抛物对流扩散方程的有限差分法[J].系统科学与数学,2009,29(7):888-901. |
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| 作者姓名： | 岑仲迪 |
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| 作者单位： | 浙江万里学院数学研究所,宁波,315100 |
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| 基金项目： | 国家自然科学基金，浙江省自然科学基金，宁波市自然科学基金 |
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| 摘 要： | 研究含有两个小参数的奇异摄动抛物对流扩散方程的有限差分法.应用极大模原理和障碍函数技巧,可得方程的准确解及其各阶导数的界的估计.基于准确解的有关性态, 构造分片一致的Shishkin型网格.在Shishkin型网格上构建一个隐式迎风差分格式来进行数值求解,证得此差分策略是关于两个小参数都一致一阶收敛的.数值实验证实了理论结果的正确性.
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| 关 键 词： | 奇异摄动 对流扩散 有限差分法 Shishkin 网格 一致收敛. |
| 收稿时间： | 2008-9-11 |
ANALYSIS OF A FINITE DIFFERENCE SCHEME FOR A PARABOLIC CONVECTION-DIFFUSION PROBLEM WITH TWO SMALL PARAMETERS |
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| CEN Zhongdi.ANALYSIS OF A FINITE DIFFERENCE SCHEME FOR A PARABOLIC CONVECTION-DIFFUSION PROBLEM WITH TWO SMALL PARAMETERS[J].Journal of Systems Science and Mathematical Sciences,2009,29(7):888-901. |
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| Authors: | CEN Zhongdi |
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| Institution: | Institute of Mathematics, Zhejiang Wanli University, Ningbo 315100 |
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| Abstract: | In this paper a parabolic convection-diffusion problem with two small parameters is considered. By using the maximum principle with carefully chosen barrier functions, we obtain the estimates of bounds for the exact solution and itsderivatives. A fully implicit upwind finite difference scheme on a Shishkin-type mesh is used to solve the problem numerically. It is shown that the scheme converge almost first-order uniformly with respect to two small parameters. Numerical results support the theoretical results. |
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| Keywords: | Singularly perturbed convection-diffusion finite difference Shishkin mesh uniform convergence |
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