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

Advances in Difference Equations

Hong Xia¹  Zhendong Luo² 

[1] School of Control and Computer Engineering, North China Electric Power University, Beijing, China;School of Mathematics and Physics, North China Electric Power University, Beijing, China

关键词: optimized finite difference Crank-Nicolson iterative scheme;    Sobolev equation;    proper orthogonal decomposition;    stability and convergence;    numerical simulation;    65M60;    65N30;    65N15;   

DOI  :  10.1186/s13662-017-1253-8

学科分类：数学（综合）

来源: SpringerOpen

【 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.

【 授权许可】

CC BY