A semi-linear delayed diffusion-wave system with distributed order in time

Abstract

A numerical scheme for a class of non-linear distributed order fractional diffusion-wave equations with fixed time-delay is considered. The focus lies on the derivation of a linearized compact difference scheme as well as on quantitatively analyzing it. We prove unique solvability, convergence, and stability of the resulted numerical solution in L∞-norm by means of the discrete energy method. Numerical examples are introduced to illustrate the accuracy and efficiency of the proposed method. © 2017, Springer Science+Business Media New York.