An efficient technique based on cubic B-spline functions for solving time-fractional advection diffusion equation involving Atangana-Baleanu derivative.

Abstract

The present paper deals with cubic B-spline approximation together with theta -weighted scheme to obtain numerical solution of the time fractional advection diffusion equation using Atangana–Baleanu derivative. To discretize the Atangana–Baleanu time derivative containing a non-singular kernel, finite difference scheme is utilized. The cubic basis functions are associated with spatial discretization. The current discretization scheme used in the present study is unconditionally stable and the convergence is of order O(h^2+Delta t^{2}). The proposed scheme is validated through some numerical examples which reveal the current scheme is feasible and quite accurate.