(untitled) (Advances in Applied Mathematics and Mechanics, 2020)
In this paper, a linearized difference scheme is proposed for the Sine-Gordon equation (SGE) with a Caputo time derivative of order α(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_∞ norm. Finally, several numerical experiments are provided to support the theoretical results.