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 - <p style="text-align: justify;">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.</p>