A fast algorithm for two-dimensional distributed-order time-space fractional diffusion equations

作者：

Highlights：

• Two-dimensional distributed-order time-space fractional diffusion problem is considered and its finite difference discretization is studied.

• The stability and convergence of the scheme are investigated.

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

• A fast and memory saving algorithm for solving DO time-space fractional diffusion equation is developed through Gauss quadrature formula, ESA method and PCG method.

• Numerical experiments show strong effectiveness and efficiency of the method.

摘要

•Two-dimensional distributed-order time-space fractional diffusion problem is considered and its finite difference discretization is studied.•The stability and convergence of the scheme are investigated.•The spatial second-order convergence and the temporal optimal convergence are obtained.•A fast and memory saving algorithm for solving DO time-space fractional diffusion equation is developed through Gauss quadrature formula, ESA method and PCG method.•Numerical experiments show strong effectiveness and efficiency of the method.

论文关键词：Time-space fractional equation,Distributed-order fractional derivative,Fast algorithm,Block-circulant-circulant-block preconditioner,Exponential-sum-approximation method,Stability and convergence

论文评审过程：Received 24 September 2021, Revised 13 February 2022, Accepted 13 March 2022, Available online 2 April 2022, Version of Record 2 April 2022.

论文官网地址：https://doi.org/10.1016/j.amc.2022.127095