A Reduced-Order Extrapolating Finite Difference Iterative Scheme for 2D Generalized Nonlinear Sine-Gordon Equation
Applied and Computational Mathematics
Volume 7, Issue 1, February 2018, Pages: 19-25
Received: Dec. 17, 2017; Accepted: Jan. 2, 2018; Published: Jan. 18, 2018
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Authors
Hong Xia, School of Control and Computer Engineering, North China Electric Power University, Beijing, China
Fei Teng, School of Control and Computer Engineering, North China Electric Power University, Beijing, China
Zhendong Luo, School of Mathematics and Physics, North China Electric Power University, Beijing, China
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Abstract
In this study, a reduced-order extrapolating finite difference iterative (ROEFDI) scheme holding sufficiently high accuracy but containing very few degrees of freedom for the two-dimensional (2D) generalized nonlinear Sine-Gordon equation is built via the proper orthogonal decomposition. The stability and convergence of the ROEFDI solutions are analyzed. And the feasibility and effectiveness of the ROEFDI scheme are verified by numerical simulations. This means that the ROEFDI scheme is effective and feasible for finding the numerical solutions of the 2D generalized nonlinear Sine-Gordon equation.
Keywords
Reduced-Order Finite Difference Scheme, Degree of Freedom, Generalized Nonlinear Sine-Gordon Equation, Proper Orthogonal Decomposition
To cite this article
Hong Xia, Fei Teng, Zhendong Luo, A Reduced-Order Extrapolating Finite Difference Iterative Scheme for 2D Generalized Nonlinear Sine-Gordon Equation, Applied and Computational Mathematics. Vol. 7, No. 1, 2018, pp. 19-25. doi: 10.11648/j.acm.20180701.13
Copyright
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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