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

  • Eid H. Doha , Mohamed A. Abdelkawy , Ahmed Z. M. Amin und António M. Lopes EMAIL logo
Veröffentlicht/Copyright: 24. August 2021
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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.

Mathematics Subject Classification (2010): 2C05; 65D32; 65N35; 35R11

Corresponding author: António M. Lopes, UISPA–LAETA/INEGI, Faculty of Engineering, University of Porto, Porto, Portugal, E-mail:

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2021-01-16
Revised: 2021-07-14
Accepted: 2021-08-03
Published Online: 2021-08-24

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. Original Research Articles
  3. Numerical solutions for variable-order fractional Gross–Pitaevskii equation with two spectral collocation approaches
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