Year: 2021
Author: Zhiyong Xing, Liping Wen
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 2 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2019-0346
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 2 : pp. 285–295
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: Time-fractional Sine-Gordon equation Caputo fractional derivative linearized difference scheme convergence and stability.