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Volume 13, Issue 2
A Linearized Difference Scheme for Time-Fractional Sine-Gordon Equation

Zhiyong Xing & Liping Wen

DOI: 10.4208/aamm.OA-2019-0346

Adv. Appl. Math. Mech., 13 (2021), pp. 285-295.

Published online: 2020-12

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  • Abstract

In this paper, a linearized difference scheme is proposed for the Sine-Gordon equation (SGE) with a Caputo time derivative of order $\alpha\in(1,2)$. Comparing with the existing linearized difference schemes, the proposed numerical scheme is simpler and easier for theoretical analysis. The solvability, boundedness and convergence of the difference scheme are rigorously established in the $L_{\infty}$ norm. Finally, several numerical experiments are provided to support the theoretical results.

  • Keywords

Time-fractional Sine-Gordon equation, Caputo fractional derivative, linearized difference scheme, convergence and stability.

  • AMS Subject Headings

35R11, 65M06, 65M12

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

201690110064@smail.xtu.edu.cn (Zhiyong Xing)

  • BibTex
  • RIS
  • TXT
@Article{AAMM-13-285, author = {Xing , Zhiyong and Wen , Liping}, title = {A Linearized Difference Scheme for Time-Fractional Sine-Gordon Equation}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2020}, volume = {13}, number = {2}, pages = {285--295}, abstract = {

In this paper, a linearized difference scheme is proposed for the Sine-Gordon equation (SGE) with a Caputo time derivative of order $\alpha\in(1,2)$. Comparing with the existing linearized difference schemes, the proposed numerical scheme is simpler and easier for theoretical analysis. The solvability, boundedness and convergence of the difference scheme are rigorously established in the $L_{\infty}$ norm. Finally, several numerical experiments are provided to support the theoretical results.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0346}, url = {http://global-sci.org/intro/article_detail/aamm/18484.html} }
TY - JOUR T1 - A Linearized Difference Scheme for Time-Fractional Sine-Gordon Equation AU - Xing , Zhiyong AU - Wen , Liping JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 285 EP - 295 PY - 2020 DA - 2020/12 SN - 13 DO - http://doi.org/10.4208/aamm.OA-2019-0346 UR - https://global-sci.org/intro/article_detail/aamm/18484.html KW - Time-fractional Sine-Gordon equation, Caputo fractional derivative, linearized difference scheme, convergence and stability. AB -

In this paper, a linearized difference scheme is proposed for the Sine-Gordon equation (SGE) with a Caputo time derivative of order $\alpha\in(1,2)$. Comparing with the existing linearized difference schemes, the proposed numerical scheme is simpler and easier for theoretical analysis. The solvability, boundedness and convergence of the difference scheme are rigorously established in the $L_{\infty}$ norm. Finally, several numerical experiments are provided to support the theoretical results.

Xing , Zhiyong and Wen , Liping. (2020). A Linearized Difference Scheme for Time-Fractional Sine-Gordon Equation. Advances in Applied Mathematics and Mechanics. 13 (2). 285-295. doi:10.4208/aamm.OA-2019-0346
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