A Compact Difference Scheme for Time-Space Fractional Nonlinear Diffusion-Wave Equations with Initial Singularity  

作　　者：Emadidin Gahalla Mohmed Elmahdi Sadia Arshad Jianfei Huang 

机构地区：[1]College of Mathematical Sciences,Yangzhou University,Yangzhou,Jiangsu 225002,China [2]Faculty of Education,University of Khartoum,Khartoum P.O.Box 321,Sudan [3]COMSATS University Islamabad,Lahore Campus,Pakistan

出　　处：《Advances in Applied Mathematics and Mechanics》2024年第1期146-163,共18页应用数学与力学进展（英文）

基　　金：supported by Natural Science Foundation of Jiangsu Province of China(Grant No.BK20201427);National Natural Science Foundation of China(Grant Nos.11701502 and 11871065)。

摘　　要：In this paper,we present a linearized compact difference scheme for onedimensional time-space fractional nonlinear diffusion-wave equations with initial boundary value conditions.The initial singularity of the solution is considered,which often generates a singular source and increases the difficulty of numerically solving the equation.The Crank-Nicolson technique,combined with the midpoint formula and the second-order convolution quadrature formula,is used for the time discretization.To increase the spatial accuracy,a fourth-order compact difference approximation,which is constructed by two compact difference operators,is adopted for spatial discretization.Then,the unconditional stability and convergence of the proposed scheme are strictly established with superlinear convergence accuracy in time and fourth-order accuracy in space.Finally,numerical experiments are given to support our theoretical results.

关 键 词：Fractional nonlinear diffusion-wave equations finite difference method fourth-order compact operator STABILITY CONVERGENCE 

分 类 号：O17[理学—数学]