An Efficient Discrete Model to Approximate the Solutions of a Nonlinear Double-Fractional Two-Component Gross–Pitaevskii-Type System

Jorge E. Macías-Díaz, Nuria Reguera and Adán J. Serna-Reyes
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Jorge E. Macías-Díaz: Department of Mathematics and Didactics of Mathematics, School of Digital Technologies, Tallinn University, 10120 Tallinn, Estonia
Nuria Reguera: Departamento de Matemáticas y Computación, Universidad de Burgos, IMUVA, 09001 Burgos, Spain
Adán J. Serna-Reyes: Centro de Ciencias Básicas, Universidad Autónoma de Aguascalientes, Aguascalientes 20131, Mexico

Mathematics, 2021, vol. 9, issue 21, 1-14

Abstract: In this work, we introduce and theoretically analyze a relatively simple numerical algorithm to solve a double-fractional condensate model. The mathematical system is a generalization of the famous Gross–Pitaevskii equation, which is a model consisting of two nonlinear complex-valued diffusive differential equations. The continuous model studied in this manuscript is a multidimensional system that includes Riesz-type spatial fractional derivatives. We prove here the relevant features of the numerical algorithm, and illustrative simulations will be shown to verify the quadratic order of convergence in both the space and time variables.

Keywords: fractional Bose–Einstein model; double-fractional system; fully discrete model; stability and convergence analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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