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Volume 9, Issue 4
Numerical Simulation for the Variable-Order Fractional Schrödinger Equation with the Quantum Riesz-Feller Derivative

N. H. Sweilam & M. M. Abou Hasan

DOI: 10.4208/aamm.2015.m1312

Adv. Appl. Math. Mech., 9 (2017), pp. 990-1011.

Published online: 2018-05

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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 equation, quantum Riesz-Feller variable-order definition, weighted average non-standard finite difference method, Jon von Neumann stability analysis.

  • AMS Subject Headings

65M06, 65M12, 34A08

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-9-990, author = {Sweilam , N. H. and Abou Hasan , M. M.}, title = {Numerical Simulation for the Variable-Order Fractional Schrödinger Equation with the Quantum Riesz-Feller Derivative}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {9}, number = {4}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2015.m1312}, url = {http://global-sci.org/intro/article_detail/aamm/12186.html} }
TY - JOUR T1 - Numerical Simulation for the Variable-Order Fractional Schrödinger Equation with the Quantum Riesz-Feller Derivative AU - Sweilam , N. H. AU - Abou Hasan , M. M. JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 990 EP - 1011 PY - 2018 DA - 2018/05 SN - 9 DO - http://doi.org/10.4208/aamm.2015.m1312 UR - https://global-sci.org/intro/article_detail/aamm/12186.html KW - Variable-order Schrödinger equation, quantum Riesz-Feller variable-order definition, weighted average non-standard finite difference method, Jon von Neumann stability analysis. AB -

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.

Sweilam , N. H. and Abou Hasan , M. M.. (2018). Numerical Simulation for the Variable-Order Fractional Schrödinger Equation with the Quantum Riesz-Feller Derivative. Advances in Applied Mathematics and Mechanics. 9 (4). 990-1011. doi:10.4208/aamm.2015.m1312
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