Digital Library of Zielona Góra contains 9 272 digital objects
Object
Title: A conservative scheme with optimal error estimates for a multidimensional space-fractional Gross-Pitaevskii equation
Contributor:
Clempner, Julio B. - ed. ; Ikonen, Enso - ed. ; Kurdyukov, Alexander P. - ed.
Subtitle:
Group publication title:
Abstract:
The present work departs from an extended form of the classical multi-dimensional Gross-Pitaevskii equation, which considers fractional derivatives of the Riesz type in space, a generalized potential function and angular momentum rotation. It is well known that the classical system possesses functionals which are preserved throughout time. It is easy to check that the generalized fractional model considered in this work also possesses conserved quantities, whence the development of conservative and efficient numerical schemes is pragmatically justified. ; Motivated by these facts, we propose a finite-difference method based on weighted-shifted Grünwald differences to approximate the solutions of the generalized Gross-Pitaevskii system. We provide here a discrete extension of the uniform Sobolev inequality to multiple dimensions, and show that the proposed method is capable of preserving discrete forms of the mass and the energy of the model. Moreover, we establish thoroughly the stability and the convergence of the technique, and provide some illustrative simulations to show that the method is capable of preserving the total mass and the total energy of the generalized system.
Publisher:
Zielona Góra: Uniwersytet Zielonogórski
Resource Identifier:
DOI:
Pages:
Source:
AMCS, volume 29, number 4 (2019) ; click here to follow the link
Language:
License CC BY 4.0:
Rights:
Biblioteka Uniwersytetu Zielonogórskiego
Object collections:
- Repository > Faculties > Faculty of Computer, Electrical and Control Engineering
- Repository > Types of work > Articles
- Repository > Scientific journals and UZ publishing series > International Journal of Applied Mathematics and Computer Science (AMCS) > International Journal of Applied Mathematics and Computer Science (AMCS) (2019)
Last modified:
Jul 14, 2025
In our library since:
Jul 14, 2025
Number of object content hits:
11
All available object's versions:
https://zbc.uz.zgora.pl/repozytorium/publication/101035
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 29, number 1 (2019)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 29, number 2 (2019)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 29, number 3 (2019)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 29, number 4 (2019)
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| Edition name | Date |
|---|---|
| A conservative scheme with optimal error estimates for a multidimensional space-fractional Gross-Pitaevskii equation | Jul 14, 2025 |
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