Numerical algorithm based on an implicit fully discrete local discontinuous Galerkin method for the fractional diffusion-wave equation

In this paper, we consider the numerical approximation for the fractional diffusion-wave equation. The main purpose of this paper is to solve and analyze this problem by introducing an implicit fully discrete local discontinuous Galerkin method. The method is based on a finite difference scheme in time and local discontinuous Galerkin methods in space. By choosing the numerical fluxes carefully we prove that our scheme is unconditionally stable and get L ₂ error estimates of \(O(h^{k+1}+(\Delta t)^{2}+(\Delta t)^{\frac {\alpha }{2}}h^{k+1})\) . Finally numerical examples are performed to illustrate the efficiency and the accuracy of the method.