Sixth-order non-uniform combined compact difference scheme for multi-term time fractional diffusion-wave equation

In this paper, we propose a high-order scheme for the numerical solution of multi term time fractional diffusion-wave (FDW) equation in one and two-dimensional on non-uniform grids. Based on the sixth-order non-uniform combined compact difference (NCCD) scheme in the space directions on non-uniform grids, an alternating direction implicit (ADI) method is proposed to split the equation into two separate one dimensional equations. The multi-term time fractional derivation is described in the Caputo's sense with scheme of order O (tau(3-alpha)) 1 < alpha < 2. A numerical analysis of Fourier analysis completed by stability calculations in terms of semi-discrete eigenvalue problems are proposed. The advantage of the non-uniform combined compact difference (NCCD) scheme is that it can decrease the CPU time in comparison with the uniform combined compact difference (CCD) scheme. The sixth-order accuracy in the space directions on non-uniform grids has not been achieved in previous studies. (C) 2018 IMACS. Published by Elsevier B.V. All rights reserved.