A Nonstandard Dynamically Consistent Numerical Scheme Applied to Obesity Dynamics
The obesity epidemic is considered a health concern of paramount importance in modern society. In this work, a nonstandard finite difference scheme has been developed with the aim to solve numerically a mathematical model for obesity population dynamics. This interacting population model represented...
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2008/640154 |
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| author | Rafael J. Villanueva Abraham J. Arenas Gilberto González-Parra |
| author_facet | Rafael J. Villanueva Abraham J. Arenas Gilberto González-Parra |
| author_sort | Rafael J. Villanueva |
| collection | DOAJ |
| description | The obesity epidemic is considered a health concern of paramount importance
in modern society. In this work, a nonstandard finite difference
scheme has been developed with the aim to solve numerically a mathematical
model for obesity population dynamics. This interacting population
model represented as a system of coupled nonlinear ordinary differential
equations is used to analyze, understand, and predict the dynamics of obesity
populations. The construction of the proposed discrete scheme is developed
such that it is dynamically consistent with the original differential
equations model. Since the total population in this mathematical model
is assumed constant, the proposed scheme has been constructed to satisfy
the associated conservation law and positivity condition. Numerical
comparisons between the competitive nonstandard scheme developed here
and Euler's method show the effectiveness of the proposed nonstandard
numerical scheme. Numerical examples show that the nonstandard difference
scheme methodology is a good option to solve numerically different
mathematical models where essential properties of the populations need to
be satisfied in order to simulate the real world. |
| format | Article |
| id | doaj-art-4d45c0c8e79640e589f9f3a89b2c1419 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-4d45c0c8e79640e589f9f3a89b2c14192025-02-03T01:31:12ZengWileyJournal of Applied Mathematics1110-757X1687-00422008-01-01200810.1155/2008/640154640154A Nonstandard Dynamically Consistent Numerical Scheme Applied to Obesity DynamicsRafael J. Villanueva0Abraham J. Arenas1Gilberto González-Parra2Instituto de Matemática Multidisciplinar, Universidad Politécnica de Valencia, Edificio 8G, 2a, P.O. Box 22012, Camino de Vera s/n, 46022 Valencia, SpainDepartamento de Matemática Aplicada, Universidad de Córdoba, Montería, Ciudad Universitaria Carrera 6 No. 76-103, CP 354, Montería, ColombiaDepartamento de Cálculo, Universidad de los Andes, Mérida 5101, VenezuelaThe obesity epidemic is considered a health concern of paramount importance in modern society. In this work, a nonstandard finite difference scheme has been developed with the aim to solve numerically a mathematical model for obesity population dynamics. This interacting population model represented as a system of coupled nonlinear ordinary differential equations is used to analyze, understand, and predict the dynamics of obesity populations. The construction of the proposed discrete scheme is developed such that it is dynamically consistent with the original differential equations model. Since the total population in this mathematical model is assumed constant, the proposed scheme has been constructed to satisfy the associated conservation law and positivity condition. Numerical comparisons between the competitive nonstandard scheme developed here and Euler's method show the effectiveness of the proposed nonstandard numerical scheme. Numerical examples show that the nonstandard difference scheme methodology is a good option to solve numerically different mathematical models where essential properties of the populations need to be satisfied in order to simulate the real world.http://dx.doi.org/10.1155/2008/640154 |
| spellingShingle | Rafael J. Villanueva Abraham J. Arenas Gilberto González-Parra A Nonstandard Dynamically Consistent Numerical Scheme Applied to Obesity Dynamics Journal of Applied Mathematics |
| title | A Nonstandard Dynamically Consistent Numerical Scheme Applied to Obesity Dynamics |
| title_full | A Nonstandard Dynamically Consistent Numerical Scheme Applied to Obesity Dynamics |
| title_fullStr | A Nonstandard Dynamically Consistent Numerical Scheme Applied to Obesity Dynamics |
| title_full_unstemmed | A Nonstandard Dynamically Consistent Numerical Scheme Applied to Obesity Dynamics |
| title_short | A Nonstandard Dynamically Consistent Numerical Scheme Applied to Obesity Dynamics |
| title_sort | nonstandard dynamically consistent numerical scheme applied to obesity dynamics |
| url | http://dx.doi.org/10.1155/2008/640154 |
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