Numerical solutions for variable-order fractional Gross–Pitaevskii equation with two spectral collocation approaches

Author:

Doha Eid H.1,Abdelkawy Mohamed A.23,Amin Ahmed Z. M.3,Lopes António M.4

Affiliation:

1. Department of Mathematics, Faculty of Science , Cairo University , Giza , Egypt

2. Department of Mathematics and Statistics, College of Science , Al-Imam Mohammad Ibn Saud Islamic University (IMSIU) , Riyadh , Saudi Arabia

3. Department of Mathematics, Faculty of Science , Beni-Suef University , Beni-Suef , Egypt

4. UISPA–LAETA/INEGI, Faculty of Engineering , University of Porto , Porto , Portugal

Abstract

Abstract This paper addresses the numerical solution of multi-dimensional variable-order fractional Gross–Pitaevskii equations (VOF-GPEs) with initial and boundary conditions. A new scheme is proposed based on the fully shifted fractional Jacobi collocation method and adopting two independent approaches: (i) the discretization of the space variable and (ii) the discretization of the time variable. A complete theoretical formulation is presented and numerical examples are given to illustrate the performance and efficiency of the new algorithm. The superiority of the scheme to tackle VOF-GPEs is revealed, even when dealing with nonsmooth time solutions.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Physics and Astronomy,Mechanics of Materials,Engineering (miscellaneous),Modeling and Simulation,Computational Mechanics,Statistical and Nonlinear Physics

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