Numerical simulation for time-fractional diffusion-wave equations with time delay

In this paper, compact finite difference schemes with (3-α)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(3-\alpha )$$\end{document}-th order accuracy in time and fourth order accuracy in space based on the L1 method are constructed for time-fractional diffusion-wave equations with time delay, where α∈(1,2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha \in (1,2)$$\end{document} is the fractional order. When solving the two dimensional situation, we adopt the alternating direction implicit (ADI) method to improve the computing efficiency. The convergence and stability of the difference schemes are proved based on some crucial skills. In the end, some numerical examples demonstrate our theoretical statement.