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

LUO Zhen-dong; ZHANG Bo

doi:10.3879/j.issn.1000-0887.2016.01.009

Volume 37 Issue 1

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LUO Zhen-dong, ZHANG Bo. A Reduced-Order Extrapolating Finite Difference Algorithm Based on the POD Method for Sobolev Equations[J]. Applied Mathematics and Mechanics, 2016, 37(1): 107-116. doi: 10.3879/j.issn.1000-0887.2016.01.009

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

doi: 10.3879/j.issn.1000-0887.2016.01.009

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

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

Received Date: 2015-11-02
Rev Recd Date: 2015-11-11
Publish Date: 2016-01-16

Abstract

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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References(23)

References

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