A novel high-order ADI method for 3D fractionalconvection–diffusion equations. (August 2015) - Zhai, Shuying; Gui, Dongwei; Huang, Pengzhan; Feng, Xinlong
Abstract: In this paper, a novel high-order alternating direction implicit (ADI) method is proposed for the three-dimensional (3D) fractional convection–diffusion equation with a temporal fractional-derivative α  ∈ (0,  1). In order to keep the fourth order accuracy to approximate the second order derivatives and the desirable tridiagonal nature of the finite difference equations, we first propose a transformation to eliminate the convection terms. Then the Riemann–Liouville fractional integral operator is used to eliminate the temporal fractional-derivative. Finally, two ADI schemes with convergence order O τ min 1 + 2 α, 2 + h 4 and O τ 2 + h 4 are established respectively, where τ and h are the temporal and spatial step sizes. Numerical experiments are presented to show the high accuracy of the new method in comparison with the related works.