An optimized finite difference Crank-Nicolson iterative scheme for the 2D Sobolev equation

被引：0
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作者：
Hong Xia
Zhendong Luo
机构：
[1] North China Electric Power University,School of Control and Computer Engineering
[2] North China Electric Power University,School of Mathematics and Physics
来源：
Advances in Difference Equations | / 2017卷
关键词：
optimized finite difference Crank-Nicolson iterative scheme; Sobolev equation; proper orthogonal decomposition; stability and convergence; numerical simulation; 65M60; 65N30; 65N15;
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摘要：
In this paper, we devote ourselves to establishing the unconditionally stable and absolutely convergent optimized finite difference Crank-Nicolson iterative (OFDCNI) scheme containing very few degrees of freedom but holding sufficiently high accuracy for the two-dimensional (2D) Sobolev equation by means of the proper orthogonal decomposition (POD) technique, analyzing the stability and convergence of the OFDCNI solutions and using the numerical simulations to verify the feasibility and effectiveness of the OFDCNI scheme.
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