期刊名称：International Journal of Applied Mathematics and Computer Science
电子版ISSN：2083-8492
出版年度：2019
卷号：29
期号：4
页码：1-11
DOI：10.2478/amcs-2019-0053
出版社：De Gruyter Open
摘要：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 finitedifference
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.
