A Fully Discrete LDG Method for the Distributed-Order Time-Fractional Reaction-Diffusion Equation

In this paper, the numerical approximation of the distributed-order time-fractional reaction-diffusion equation is proposed and analyzed. Based on the finite difference method in time and local discontinuous Galerkin method in space, we develop a fully discrete scheme and prove that the scheme is unconditionally stable and convergent with order Ot)2+4</mml:mfenced>, where h,k,t and are the space-step size, piecewise polynomial degree, time-step size, step size in distributed-order variable, respectively. Numerical examples are presented to show the effectiveness and the accuracy of the numerical scheme.