TY - JOUR
T1 - A Compact Difference Scheme for Time-Space Fractional Nonlinear Diffusion-Wave Equations with Initial Singularity
AU - Mohmed Elmahdi , Emadidin Gahalla
AU - Arshad , Sadia
AU - Huang , Jianfei
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 146
EP - 163
PY - 2023
DA - 2023/12
SN - 16
DO - http://doi.org/10.4208/aamm.OA-2022-0049
UR - https://global-sci.org/intro/article_detail/aamm/22293.html
KW - Fractional nonlinear diffusion-wave equations, finite difference method, fourth-order compact operator, stability, convergence.
AB - <p style="text-align: justify;">In this paper, we present a linearized compact difference scheme for one-dimensional 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.</p>