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

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∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$L_{\infty }$\end{document}-norm by means of the discrete energy method. Numerical examples are introduced to illustrate the accuracy and efficiency of the proposed method.