Sobolev方程基于POD的降阶外推差分算法

罗振东; 张博

doi:10.3879/j.issn.1000-0887.2016.01.009

Sobolev方程基于POD的降阶外推差分算法

doi: 10.3879/j.issn.1000-0887.2016.01.009

罗振东,
张博

华北电力大学数理学院, 北京 102206

基金项目: 国家自然科学基金(11271127)

详细信息

作者简介:
罗振东(1958—), 男, 教授，博士, 博士生导师(通讯作者. E-mail: zhdluo@ncepu.edu.cn).

中图分类号: O242.21
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- 被引次数: 0
出版历程
- 收稿日期: 2015-11-02
- 修回日期: 2015-11-11
- 刊出日期: 2016-01-16

A Reduced-Order Extrapolating Finite Difference Algorithm Based on the POD Method for Sobolev Equations

School of Mathematics and Physics, North China Electric Power University, Beijing 102206, P.R.China

Funds: The National Natural Science Foundation of China (11271127)

摘要

摘要: 用奇异值分解和特征投影分解(proper orthogonal decomposition, 简记POD)方法建立Sobolev方程的一种降阶外推有限差分算法, 并给出误差估计.最后用数值例子，验证基于POD方法降阶外推有限差分算法的可行性和有效性.
- 奇异值分解 /
- 特征投影分解 /
- Sobolev方程 /
- 降阶外推有限差分算法
Abstract: The singular value decomposition technique and the proper orthogonal decomposition (POD) method were applied to establish a reduced-order extrapolating finite difference algorithm for Sobolev equations. Firstly, the absolutely stable fully 2nd-order accurate Crank-Nicolson (C-N) scheme for Sobolev equations was built, and the C-N reduced-order extrapolating finite difference algorithm was constructed based on the POD method, where the number of unknowns in numerical computation was greatly reduced. Secondly, the error estimates of the reduced-order finite difference solutions were provided. Finally, a numerical example was used to verify the feasibility and efficiency of the proposed reduced-order extrapolating finite difference algorithm.
- singular value decomposition /
- proper orthogonal decomposition /
- Sobolev equation /
- reduced-order extrapolating finite difference algorithm

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参考文献(23)

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