Analysis of local discontinuous Galerkin method for time-space fractional sine-Gordon equations

Abstract

The aim of the present paper is to introduce a numerical method for time-space fractional sine-Gordon equation. The fractional derivative on the space and on the time are considered in the sense of Reimann–Liouville (of order 1≤β≤2) and in the sense of Caputo (of variable order 1≤α(t)<2), respectively. The basic idea is to apply local discontinuous Galerkin method in space and a finite difference method in time. The stability and convergence analysis of the method are presented. Numerical results show that the accuracy and reliability of the proposed method for time-space fractional sine-Gordon equation.