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.
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 onthe 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.
出处
《应用数学和力学》
CSCD
北大核心
2016年第1期107-116,共10页
Applied Mathematics and Mechanics
基金
国家自然科学基金(11271127)~~
关键词
奇异值分解
特征投影分解
SOBOLEV方程
降阶外推有限差分算法
singular value decomposition
proper orthogonal decomposition
Sobolev equation
reduced-order extrapolating finite difference algorithm