Numerical solution for a sub-diffusion equation with a smooth kernel

In this paper we study the numerical solution of an initial value problem of a sub-diffusion type. For the time discretization we apply the discontinuous Galerkin method and we use continuous piecewise finite elements for the space discretization. Optimal order convergence rates of our numerical solution have been shown. We compare our theoretical error bounds with the results of numerical computations. We also present some numerical results showing the super-convergence rates of the proposed method.