An efficient alternating segment parallel finite difference method for multi-term time fractional diffusion-wave equation

The multi-term time fractional diffusion-wave equation is of important physical meaning and engineering application value. In order to meet the needs of fast solving multi-term time fractional diffusion-wave equation, an efficient difference algorithm with intrinsic parallelism is proposed in this paper. The alternating segment Crank–Nicolson (ASC-N) parallel difference scheme is constructed with four kinds of Saul’yev asymmetric schemes and the classical Crank–Nicolson (C–N) scheme, based on alternating segment technology. The theoretical analysis shows that the ASC-N scheme is second-order convergence in space and 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} order convergence in time.The computing efficiency of the ASC-N scheme can save about 80% for C–N scheme when the number of space grids is large. The theoretical analysis and numerical experiments show that the ASC-N method is effective for solving multi-term time fractional diffusion-wave equation.