And agreed to the published version of the manuscript. Funding: This
And agreed towards the published version from the manuscript. Funding: This study was partially supported by University of Basilicata (neighborhood funds) and by GNCS Project 2020 “Approssimazione multivariata ed equazioni funzionali per la modellistica numerica”. Acknowledgments: The authors thank the anonymous referees for their ideas and remarks, which permitted to improve the paper. The research has been accomplished inside “Research ITalianMathematics 2021, 9,18 ofnetwork on Approximation” (RITA). Each of the authors are members of the INdAM-GNCS Investigation Group. The second and third authors are members in the TAA-UMI Analysis Group. Conflicts of Interest: The authors declare no conflict of interest.
mathematicsArticleAn Efficient Discrete Model to Approximate the Solutions of a Nonlinear Double-Fractional Two-Component Gross itaevskii-Type SystemJorge E. Mac s-D z 1,two, , Nuria Regueraand Ad J. Serna-ReyesDepartment of Mathematics and Didactics of Mathematics, College of Goralatide Protocol Digital Technologies, Tallinn University, 10120 Tallinn, Estonia Departamento de Matem icas y F ica, Universidad Aut oma de Aguascalientes, Aguascalientes 20131, Mexico Departamento de Matem icas y Computaci , Universidad de Burgos, IMUVA, 09001 Burgos, Spain; [email protected] Centro de Ciencias B icas, Universidad Aut oma de Aguascalientes, Aguascalientes 20131, Mexico; [email protected] Correspondence: [email protected] or [email protected]; Tel.: +52-449-Citation: Mac s-D z, J.E.; Reguera, N.; Serna-Reyes, A.J. An Effective Discrete Model to Approximate the Solutions of a Nonlinear Double-Fractional Two-Component Gross itaevskii-Type Method. Mathematics 2021, 9, 2727. https:// doi.org/10.3390/mathAbstract: In this work, we introduce and theoretically analyze a fairly simple numerical algorithm to resolve a double-fractional condensate model. The mathematical system can be a generalization of the popular Gross itaevskii equation, which is a model consisting of two nonlinear complexvalued diffusive differential equations. The continuous model studied in this manuscript is really a multidimensional system that involves Riesz-type spatial fractional derivatives. We prove here the relevant capabilities in the numerical algorithm, and illustrative simulations will likely be shown to verify the quadratic order of convergence in each the space and time variables. Dataset License: CC-BY-NC. Key phrases: fractional Bose GSK2646264 web instein model; double-fractional system; totally discrete model; stability and convergence evaluation MSC: 65Mxx; 65QxxAcademic Editors: Bego Cano and Mechthild Thalhammer Received: 7 October 2021 Accepted: 19 October 2021 Published: 27 October1. Introduction There have been dramatic developments in the area of fractional calculus in current decades [1], and numerous regions in applied and theoretical mathematics have benefited from these developments [2,3]. In particular, there have been substantial developments inside the theory and application of numerical techniques for fractional partial differential equations. One example is, from a theoretical point of view, theoretical analyses of conservative finitedifference schemes to solve the Riesz space-fractional Gross itaevskii program have been proposed in the literature [4], along with convergent three-step numerical approaches to solve double-fractional condensates, explicit dissipation-preserving solutions for Riesz space-fractional nonlinear wave equations in numerous dimensions [5], power conservative distinction schemes for nonlinear fractional S.
