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 - <p style="text-align: justify;">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.</p>