Some reduced finite difference schemes based on a proper orthogonal decomposition technique for parabolic equations

Authors:
Ping Sun;Zhendong Luo;Yanjie Zhou
Affiliations:
School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, China;School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China;College of Computer and Information Engineering, Beijing Technology and Business University, Beijing 100037, China
Venue:
Applied Numerical Mathematics
Year:
2010

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Abstract

In this paper, some reduced finite difference schemes based on a proper orthogonal decomposition (POD) technique for parabolic equations are derived. Also the error estimates between the POD approximate solutions of the reduced finite difference schemes and the exact solutions for parabolic equations are established. It is shown by considering the results of two numerical examples that the numerical results are consistent with theoretical conclusions. Moreover, it is also shown that the POD reduced finite difference schemes are feasible and efficient.