A Nonstandard Dynamically Consistent Numerical Scheme Applied to Obesity Dynamics

• Published in: Journal of applied mathematics 2008, Vol.2008 (2008), p.1-14
• Main Authors: Villanueva Micó, Rafael Jacinto, Arenas, Abraham J., González-Parra, Gilberto
• Format: Article
• Language: English
• ISSN: 1110-757X; 1687-0042

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.