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