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

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 diffe...

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Autores principales:	Jorge E. Macías-Díaz, Nuria Reguera, Adán J. Serna-Reyes
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	fractional Bose–Einstein model double-fractional system fully discrete model stability and convergence analysis Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/44e97b00a5a545d29573905cd60c9526
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spelling	oai:doaj.org-article:44e97b00a5a545d29573905cd60c95262021-11-11T18:16:48ZAn Efficient Discrete Model to Approximate the Solutions of a Nonlinear Double-Fractional Two-Component Gross–Pitaevskii-Type System10.3390/math92127272227-7390https://doaj.org/article/44e97b00a5a545d29573905cd60c95262021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2727https://doaj.org/toc/2227-7390In 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.Jorge E. Macías-DíazNuria RegueraAdán J. Serna-ReyesMDPI AGarticlefractional Bose–Einstein modeldouble-fractional systemfully discrete modelstability and convergence analysisMathematicsQA1-939ENMathematics, Vol 9, Iss 2727, p 2727 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	fractional Bose–Einstein model double-fractional system fully discrete model stability and convergence analysis Mathematics QA1-939
spellingShingle	fractional Bose–Einstein model double-fractional system fully discrete model stability and convergence analysis Mathematics QA1-939 Jorge E. Macías-Díaz Nuria Reguera Adán J. Serna-Reyes An Efficient Discrete Model to Approximate the Solutions of a Nonlinear Double-Fractional Two-Component Gross–Pitaevskii-Type System
description	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.
format	article
author	Jorge E. Macías-Díaz Nuria Reguera Adán J. Serna-Reyes
author_facet	Jorge E. Macías-Díaz Nuria Reguera Adán J. Serna-Reyes
author_sort	Jorge E. Macías-Díaz
title	An Efficient Discrete Model to Approximate the Solutions of a Nonlinear Double-Fractional Two-Component Gross–Pitaevskii-Type System
title_short	An Efficient Discrete Model to Approximate the Solutions of a Nonlinear Double-Fractional Two-Component Gross–Pitaevskii-Type System
title_full	An Efficient Discrete Model to Approximate the Solutions of a Nonlinear Double-Fractional Two-Component Gross–Pitaevskii-Type System
title_fullStr	An Efficient Discrete Model to Approximate the Solutions of a Nonlinear Double-Fractional Two-Component Gross–Pitaevskii-Type System
title_full_unstemmed	An Efficient Discrete Model to Approximate the Solutions of a Nonlinear Double-Fractional Two-Component Gross–Pitaevskii-Type System
title_sort	efficient discrete model to approximate the solutions of a nonlinear double-fractional two-component gross–pitaevskii-type system
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/44e97b00a5a545d29573905cd60c9526
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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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