Numerical solutions for 2-D fractional Schr¨odinger equation with the Riesz–Feller derivative

What is it about?

In this paper, we present an accurate numerical method for solving a space-fractional Schr¨odinger 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.

Featured Image

Why is it important?

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