Difference numerical solutions for time-space fractional advection diffusion equation

Fangfang Zhang, Xiaoyang Gao, Zhaokun Xie
2019 Boundary Value Problems  
In this paper, a time-space fractional advection diffusion equation is considered for the natural extension of the convection diffusion equation. An explicit difference scheme and an implicit difference scheme are presented. The stability and convergence of the two difference schemes are discussed. It is shown that the explicit difference scheme is conditionally stable and convergent, and the implicit difference scheme is unconditionally stable and convergent. The convergence order of the two
more » ... order of the two methods is O(τ + h).
doi:10.1186/s13661-019-1120-5 fatcat:inihbciy45fkbjyav2gx5yj5am