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

- A novel weighted average non-standard finite difference method is presented.
- Numerical simulations for the space fractional Schrödinger equation.
- The fractional derivative is defined by the quantum Riesz-Feller fractional derivative.

In this paper, we present an accurate numerical method for solving a space-fractional Schrödinger 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 α,where 1<α≤2 and of skewness θ. Experimental findings indicate that the proposed method is easy to implement, effective and convenient for solving the proposed model.