Numerical solutions for variable-order fractional Gross–Pitaevskii equation with two spectral collocation approaches-Reference-Cited by-同舟云学术

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

Published:2021-08-24 Issue:0 Volume:0 Page:
ISSN:1565-1339
Container-title:International Journal of Nonlinear Sciences and Numerical Simulation
language:en
Short-container-title:

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

Link

https://www.degruyter.com/document/doi/10.1515/ijnsns-2021-0018/pdf

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