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

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  • Jorge E. Macías-Díaz

    (Department of Mathematics and Didactics of Mathematics, School of Digital Technologies, Tallinn University, 10120 Tallinn, Estonia
    Departamento de Matemáticas y Física, Universidad Autónoma de Aguascalientes, Aguascalientes 20131, Mexico)

  • 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)

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.

Suggested Citation

  • Jorge E. Macías-Díaz & Nuria Reguera & Adán J. Serna-Reyes, 2021. "An Efficient Discrete Model to Approximate the Solutions of a Nonlinear Double-Fractional Two-Component Gross–Pitaevskii-Type System," Mathematics, MDPI, vol. 9(21), pages 1-14, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2727-:d:666228
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    References listed on IDEAS

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    1. Manuel Duarte Ortigueira, 2006. "Riesz potential operators and inverses via fractional centred derivatives," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2006, pages 1-12, August.
    2. X. Wang & F. Liu & X. Chen, 2015. "Novel Second-Order Accurate Implicit Numerical Methods for the Riesz Space Distributed-Order Advection-Dispersion Equations," Advances in Mathematical Physics, Hindawi, vol. 2015, pages 1-14, November.
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