In this paper, the Laplace transform combined with the local
discontinuous Galerkin method is used for distributed-order
time-fractional diffusion-wave equation. In this method,at first, we
convert the equation to some time-independent problems by Laplace
transform.Then we can solve these stationary equations by the local
discontinuous Galerkin method to discretize diffusion operators at the
same time. Then, by using a numerical inversion of the Laplace transform
we can find the solutions of the original equation. One of the
advantages of this procedure is its parallel implementation. Another
advantage of this approach is that the number of stationary problems
that should be solved is much less than that are needed in time-marching
methods. Finally, some numerical experiments have been provided to show
the accuracy and efficiency of the method.