Compact difference scheme for distributed-order time-fractional diffusion-wave equation on bounded domains

In this paper, we derive and analyse a compact difference scheme for a distributed-order time-fractional diffusion-wave equation. This equation is approximated by a multi-term fractional diffusion-wave equation, which is then solved by a compact difference scheme. The unique solvability of the difference solution is discussed. Using the discrete energy method, we prove the compact difference scheme is unconditionally stable and convergent. Finally, numerical results are presented to support our theoretical analysis.