Numerical Simulation for the Variable-Order Fractional Schrödinger Equation with the Quantum Riesz-Feller Derivative
Year: 2017
Author: N. H. Sweilam, M. M. Abou Hasan
Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 4 : pp. 990–1011
Abstract
In this paper the space variable-order fractional Schrödinger equation (VOFSE) is studied numerically, where the variable-order fractional derivative is described here in the sense of the quantum Riesz-Feller definition. The proposed numerical method is the weighted average non-standard finite difference method (WANSFDM). Special attention is given to study the stability analysis and the convergence of the proposed method. Finally, two numerical examples are provided to show that this method is reliable and computationally efficient.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2015.m1312
Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 4 : pp. 990–1011
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Variable-order Schrödinger equation quantum Riesz-Feller variable-order definition weighted average non-standard finite difference method Jon von Neumann stability analysis.
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