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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 Gr\u00fcnwald differences to approximate the solutions of the generalized Gross\u2013Pitaevskii 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.<\/jats:p>","DOI":"10.2478\/amcs-2019-0053","type":"journal-article","created":{"date-parts":[[2020,1,8]],"date-time":"2020-01-08T09:30:32Z","timestamp":1578475832000},"page":"713-723","source":"Crossref","is-referenced-by-count":5,"title":["A Conservative Scheme with Optimal Error Estimates for a Multidimensional Space\u2013Fractional Gross\u2013Pitaevskii Equation"],"prefix":"10.61822","volume":"29","author":[{"given":"Ahmed S.","family":"Hendy","sequence":"first","affiliation":[{"name":"Department of Computational Mathematics and Computer Science , Ural Federal University , 19 Mira St., Yekaterinburg 620002 , Russia"},{"name":"Department of Mathematics, Faculty of Science , Benha University , Benha 13511 , Egypt"}]},{"given":"Jorge E.","family":"Mac\u00edas-D\u00edaz","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Physics Autonomous , University of Aguascalientes , Avenida Universidad 940 Ciudad Universitaria, Aguascalientes 20131 , Mexico"}]}],"member":"37438","published-online":{"date-parts":[[2019,12,31]]},"reference":[{"key":"2023050302360485887_j_amcs-2019-0053_ref_001_w2aab3b7b7b1b6b1ab1ab1Aa","doi-asserted-by":"crossref","unstructured":"Alikhanov, A.A. 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