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

Doha E. H., Abdelkawy M. A., AHMED ZAKI MAHAMED AMIN A. Z. M. A., Lopes A. M.

International Journal of Nonlinear Sciences and Numerical Simulation, vol.24, no.2, pp.421-435, 2023 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.1515/ijnsns-2021-0018
  • Journal Name: International Journal of Nonlinear Sciences and Numerical Simulation
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.421-435
  • Keywords: Caputo fractional derivative, spectral collocation, variable-order fractional Gross-Pitaevskii equation
  • Istanbul Gelisim University Affiliated: Yes

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.