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

摘要

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 (Delta t(1+sigma/2) + h(2) + k(2) + sigma(2)) both for pressure and velocity are established on non-uniform rectangular grids, where Delta t, h, k and sigma 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. (C) 2018 IMACS. Published by Elsevier B.V. All rights reserved.