Non-polynomial spline approach in two-dimensional fractional sub-diffusion problems

In this paper, we propose a new numerical scheme for two-dimensional fractional subdiffusion problems using non-polynomial spline. The solvability, stability and convergence of the proposed method are established using the well known discrete energy methodology. It is shown that the spatial convergence order is at least 4.5 which improves the best result achieved to date. We also carry out simulation to demonstrate the accuracy and efficiency of the proposed scheme and to compare with other methods. (c) 2019 Elsevier Inc. All rights reserved.