A compact exponential difference method for multi-term time-fractional convection-reaction-diffusion problems with non-smooth solutions

作者：

Highlights：

• Multi-term time-fractional convection-reaction-diffusion problems with non-smooth solutions are considered.

• A compact exponential finite difference method is proposed

• Taking into account the initial weak singularity of the solution, the stability and convergence of the method is rigorously proved.

• The spatial fourth-order convergence and the temporal optimal convergence are obtained.

• Numerical results confirm the theoretical convergence result.

摘要

•Multi-term time-fractional convection-reaction-diffusion problems with non-smooth solutions are considered.•A compact exponential finite difference method is proposed•Taking into account the initial weak singularity of the solution, the stability and convergence of the method is rigorously proved.•The spatial fourth-order convergence and the temporal optimal convergence are obtained.•Numerical results confirm the theoretical convergence result.

论文关键词：Fractional convection-reaction-diffusion problems,Multi-term fractional derivative,Weak singularity,Compact exponential difference method,Nonuniform time mesh

论文评审过程：Received 6 February 2020, Revised 6 April 2020, Accepted 13 April 2020, Available online 28 April 2020, Version of Record 28 April 2020.

论文官网地址：https://doi.org/10.1016/j.amc.2020.125316