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

摘要

In this paper, we investigate a fully implicit finite difference scheme for solving the time fractional advectiona??diffusion equation. The time fractional derivative is estimated using Caputoa??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.