Numerical Simulation for the Variable-Order Fractional Schrödinger Equation with the Quantum Riesz-Feller Derivative (Advances in Applied Mathematics and Mechanics, 2018)
In this paper the space variable-order fractional Schrödinger equation(VOFSE) is studied numerically, where the variable-order fractional derivative isdescribed here in the sense of the quantum Riesz-Feller definition. The proposednumerical method is the weighted average non-standard finite difference method(WANSFDM). Special attention is given to study the stability analysis and the convergenceof the proposed method. Finally, two numerical examples are provided toshow that this method is reliable and computationally efficient.