Análise numérica de sistemas dinâmicos

Abstract

The numerical analysis is a very efficient tool in the study of the behavior of dynamic systems. We have studied two systems of population dynamics modeled through ordinary differential equations and partial differential equations that do not possess analytic solutions. Initially, Euler’s first point method and Runge-Kutta of fourth order were used, they take O(h) and O(h2), for solving numerically the system of ordinary differential equations. As the numerical approaches utilized for ordinary differential equations do not apply to partial differential equations, explicit approaches and Crank-Nicholson were used for such equations. We made comparisons between the results obtained through the numerical approaches for ordinary differential equations and verified which numerical approach is the most appropriate one. The same process was carried out to detect which numerical approach is more efficient in solving partial differential equations.