In this paper, we present a numerical method for solving the one-dimensional space fractional Schr¨odinger equation in the case of a particle moving in a potential field. The fractional derivative is defined by the quantum Riesz-Feller fractional derivative. A novel weighted average non-standard finite difference method is presented to solve the underline problem numerically. The stability analysis of the proposed method is given by a recently proposed procedure similar to the standard John von Neumann stability analysis and the truncation error is analyzed. Several numerical examples are introduced for various choices of derivative order a, 1
Digital Object Identifier (DOI)
Hassan Sweilam, Nasser and Mustafa Abou Hasan, Muner
"Numerical Studies for the Fractional Schrodinger Equation with the Quantum Riesz-Feller Derivative,"
Progress in Fractional Differentiation & Applications: Vol. 2
, Article 1.
Available at: https://dc.naturalspublishing.com/pfda/vol2/iss4/1