Analysis of a new finite difference/local discontinuous Galerkin method for the fractional diffusion-wave equation

In this paper a finite difference/local discontinuous Galerkin method for the fractional diffusion-wave equation is presented and analyzed. We first propose a new finite difference method to approximate the time fractional derivatives, and give a semidiscrete scheme in time. Further we develop a fully discrete scheme for the fractional diffusion-wave equation, and prove that the method is unconditionally stable and convergent with order O(hk+1+(Δt)3−α), where k is the degree of piecewise polynomial. Extensive numerical examples are carried out to confirm the theoretical convergence rates.