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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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/21/2727 |
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| 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 |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-10T05:56:42Z |
| format | Article |
| id | doaj.art-44e97b00a5a545d29573905cd60c9526 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T05:56:42Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-44e97b00a5a545d29573905cd60c95262023-11-22T21:17:58ZengMDPI AGMathematics2227-73902021-10-01921272710.3390/math9212727An Efficient Discrete Model to Approximate the Solutions of a Nonlinear Double-Fractional Two-Component Gross–Pitaevskii-Type SystemJorge E. Macías-Díaz0Nuria Reguera1Adán J. Serna-Reyes2Department of Mathematics and Didactics of Mathematics, School of Digital Technologies, Tallinn University, 10120 Tallinn, EstoniaDepartamento de Matemáticas y Computación, Universidad de Burgos, IMUVA, 09001 Burgos, SpainCentro de Ciencias Básicas, Universidad Autónoma de Aguascalientes, Aguascalientes 20131, MexicoIn 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.https://www.mdpi.com/2227-7390/9/21/2727fractional Bose–Einstein modeldouble-fractional systemfully discrete modelstability and convergence analysis |
| spellingShingle | 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 Mathematics fractional Bose–Einstein model double-fractional system fully discrete model stability and convergence analysis |
| title | 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_short | 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 |
| topic | fractional Bose–Einstein model double-fractional system fully discrete model stability and convergence analysis |
| url | https://www.mdpi.com/2227-7390/9/21/2727 |
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