Numerical Simulation for the Variable-Order Fractional Schrödinger Equation with the Quantum Riesz-Feller Derivative

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.

Author Details

N. H. Sweilam

M. M. Abou Hasan

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