A block-centered finite difference method for the distributed-order time-fractional diffusion-wave equation

In this article, a block-centered finite difference method for the distributed-order time-fractional diffusion-wave equation with Neumann boundary condition is introduced and analyzed. The unconditional stability and the global convergence of the scheme are proved rigorously. Some a priori estimates of discrete norms with optimal order of convergence O(Δt1+σ/2+h2+k2+σ2) both for pressure and velocity are established on non-uniform rectangular grids, where Δt,h,k and σ are the step sizes in time, space in x- and y-direction, and distributed order. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis.