Numerical solutions for 2-D fractional Schrodinger equation with the Riesz-Feller derivative

In this paper, we present an accurate numerical method for solving a space-fractional Schrodinger equation in two dimensions. The quantum Riesz-Feller fractional derivative is used to define the fractional derivatives. The weighted average non-standard finite difference method is implemented to study the behavior of the model problem. The stability analysis of the proposed method is given by a recently proposed procedure similar to the standard John von Neumann stability analysis; moreover the truncation error is analyzed. Some numerical test examples are presented with variety values of derivatives of order a, where 1 < alpha <= 2 and of skewness theta. Experimental findings indicate that the proposed method is easy to implement, effective and convenient for solving the proposed model. (C) 2017 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.