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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1110-757X 1687-0042 |