A new implicit compact difference scheme for the fourth-order fractional diffusion-wave system

In this paper, a new implicit compact difference scheme is constructed for the fourth-order fractional diffusion-wave system by the method of order reduction. The temporal Caputo fractional derivative is discretized by an L1 scheme. The spatial derivative of order 4 is reduced to one of order 2 by order reduction. Then, the reduced derivative of order 2 is discretized by a difference formula of order 4. Using order reduction, two simple and accurate formulae of discretization for the derivative boundary conditions are obtained. And a new way of proving the stability and convergence of the scheme is presented in this paper. Some numerical results demonstrate the accuracy and efficiency of our new scheme.