A fully implicit finite difference scheme based on extended cubic B-splines for time fractional advection-diffusion equation

作者：Mohyud Din Syed Tauseef^*; Akram Tayyaba; Abbas Muhammad; Ismail Ahmad Izani; Ali Norhashidah H M

来源：Advances in Difference Equations, 2018, 2018(1): 109.

DOI：10.1186/s13662-018-1537-7

• Time fractional advection-diffusion equation
• Extended cubic B-spline basis functions
• Collocation method
• Stability
• Convergence

In this paper, we investigate a fully implicit finite difference scheme for solving the time fractional advection-diffusion equation. The time fractional derivative is estimated using Caputo's formulation, and the spatial derivatives are discretized using extended cubic B-spline functions. The convergence and stability of the fully implicit scheme are analyzed. Numerical experiments conducted indicate that the scheme is feasible and accurate.

• 出版日期2018-3-27