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

Advances in Difference Equations

Syed Tauseef Mohyud-Din¹  Muhammad Abbas²  Ahmad Izani Ismail³  Tayyaba Akram³  Norhashidah H. M. Ali³ 

[1] Center for Research (CFR), University of Islamabad (UoI);Department of Mathematics, University of Sargodha;School of Mathematical Sciences, Universiti Sains Malaysia;

关键词: Time fractional advection–diffusion equation;    Extended cubic B-spline basis functions;    Collocation method;    Stability;    Convergence;   

DOI  :  10.1186/s13662-018-1537-7

来源: DOAJ

【 摘 要 】

Abstract 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.

【 授权许可】

Unknown