TITLE:
A Numerical Study of Several Species Population Models
AUTHORS:
Francisco J. Sánchez-Bernabe, Maria del Rosario Escalona-Magdaleno
KEYWORDS:
Lotka-Volterra Equations, Adams-Bashfort Predictor, Adams-Moulton Corrector, Improved Euler Method, GeoGebra, Matlab
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.11 No.12,
December
26,
2023
ABSTRACT: This work considers a special case of Lotka-Volterra equations, which means that in the system of two ordinary differential equations, we take the four parameters equal to one. The reason is that we want just to illustrate the procedure to reduce that system to only one ordinary differential equation, such that we know its analytical solution. This idea will be applied to study the relations between a system of three ordinary differential equations, and a couple of partial differential equations. Lotka-Volterra equations are solved numerically by a fourth-order predictor-corrector method, which is initialized by an improved Euler method with a rather small time step because it is only a second-order algorithm. Then, it is proposed a model with three species, defined by ordinary differential equations.