Applied and Computational Mathematics

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A Reduced-Order Extrapolating Finite Difference Iterative Scheme for 2D Generalized Nonlinear Sine-Gordon Equation

Received: 17 December 2017    Accepted: 02 January 2018    Published: 18 January 2018
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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.

DOI 10.11648/j.acm.20180701.13
Published in Applied and Computational Mathematics (Volume 7, Issue 1, February 2018)
Page(s) 19-25
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Reduced-Order Finite Difference Scheme, Degree of Freedom, Generalized Nonlinear Sine-Gordon Equation, Proper Orthogonal Decomposition

References
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Author Information
  • School of Control and Computer Engineering, North China Electric Power University, Beijing, China

  • 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

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    Hong Xia, Fei Teng, Zhendong Luo. (2018). A Reduced-Order Extrapolating Finite Difference Iterative Scheme for 2D Generalized Nonlinear Sine-Gordon Equation. Applied and Computational Mathematics, 7(1), 19-25. https://doi.org/10.11648/j.acm.20180701.13

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    ACS Style

    Hong Xia; Fei Teng; Zhendong Luo. A Reduced-Order Extrapolating Finite Difference Iterative Scheme for 2D Generalized Nonlinear Sine-Gordon Equation. Appl. Comput. Math. 2018, 7(1), 19-25. doi: 10.11648/j.acm.20180701.13

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    AMA Style

    Hong Xia, Fei Teng, Zhendong Luo. A Reduced-Order Extrapolating Finite Difference Iterative Scheme for 2D Generalized Nonlinear Sine-Gordon Equation. Appl Comput Math. 2018;7(1):19-25. doi: 10.11648/j.acm.20180701.13

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  • @article{10.11648/j.acm.20180701.13,
      author = {Hong Xia and Fei Teng and Zhendong Luo},
      title = {A Reduced-Order Extrapolating Finite Difference Iterative Scheme for 2D Generalized Nonlinear Sine-Gordon Equation},
      journal = {Applied and Computational Mathematics},
      volume = {7},
      number = {1},
      pages = {19-25},
      doi = {10.11648/j.acm.20180701.13},
      url = {https://doi.org/10.11648/j.acm.20180701.13},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.acm.20180701.13},
      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.},
     year = {2018}
    }
    

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    T1  - A Reduced-Order Extrapolating Finite Difference Iterative Scheme for 2D Generalized Nonlinear Sine-Gordon Equation
    AU  - Hong Xia
    AU  - Fei Teng
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    DO  - 10.11648/j.acm.20180701.13
    T2  - Applied and Computational Mathematics
    JF  - Applied and Computational Mathematics
    JO  - Applied and Computational Mathematics
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    PB  - Science Publishing Group
    SN  - 2328-5613
    UR  - https://doi.org/10.11648/j.acm.20180701.13
    AB  - 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.
    VL  - 7
    IS  - 1
    ER  - 

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