A Linearized Difference Scheme for Time-Fractional Sine-Gordon Equation

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.