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

Part of: General theory in ordinary differential equations Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  18 January 2017

N. H. Sweilam  and
M. M. Abou Hasan
N. H. Sweilam*
Affiliation:
Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt
M. M. Abou Hasan
Affiliation:
Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt
*
*Corresponding author. Email:[email protected] (N. H. Sweilam)
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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.

Keywords

Variable-order Schrödinger equationquantum Riesz-Feller variable-order definitionweighted average non-standard finite difference methodJon von Neumann stability analysis

MSC classification

Secondary: 65M06: Finite difference methods 65M12: Stability and convergence of numerical methods 34A08: Fractional differential equations
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 4 , August 2017 , pp. 990 - 1011
Copyright
Copyright © Global-Science Press 2017 

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