Solution of space-time tempered fractional diffusion-wave equation using a high-order numerical method

At the present work, we attempt to obtain a high order numerical scheme for the solution of space-time fractional tempered diffusion-wave equation in one and two dimensional cases. For this purpose, we propose an unconditionally stable numerical scheme of order O(Tau 2) to approximate this equation in time direction. Then, we obtain the fully discrete scheme using the spectral element method in spatial directions. Well-posedness and error estimate of fully discrete scheme are given in details. Finally, to demonstrate the accuracy and efficiency of the proposed method in comparison with other schemes in the literature, the results of two test problems are presented.(c) 2022 Elsevier B.V. All rights reserved.