High-order compact finite volume scheme for the 2D multi-term time fractional sub-diffusion equation

Based on an L1 interpolation operator, a new high-order compact finite volume scheme is derived for the 2D multi-term time fractional sub-diffusion equation. It is shown that the difference scheme is unconditionally convergent and stable 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. The convergence order is O(τ2−α+h14+h24)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$O(\tau ^{2-\alpha }+h_{1}^{4}+h_{2}^{4})$\end{document}, where τ is the temporal step size and h1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$h_{1}$\end{document} is the spatial step size in one direction, h2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$h_{2}$\end{document} is the spatial step size in another direction. Two numerical examples are implemented, testifying to their efficiency and confirming their convergence order.