Técnica de perturbação utilizada para solução numérica de equações do 2º e 3º graus

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Universidade Federal de Goiás


Phenomenon that occur in the nature are essentially nonlinear and the dynamical systems theory aims to obtain a mathematical model that best represents the real physical systems, then nothing more coherent than the description or analysis of these natural phenomenon using models and techniques. In this dissertation, the technique of direct expansion for the development of two differential equations order to solve a nonlinear equation and the approximate determination of the roots of order algebraic equation higher or equal to two, was used. For this purpose, it was initially shown the development of a differential equation of motion subjected to a nonlinear damping, which is represented by the equation of Duffing – Van der Pol. Generally, it’s not easy to obtain an approximated analytical solution for this type equation, but this study was done with the purpouse of illustrating the technique used in the work, solving type solving a problem in which these techniques are routinely used to obtain a solution. Studied for application in basic education, it presents a way to obtain the approximate roots of equations of second and third degrees, using the technique of direct expansion for the sake of comparison. Since there are formulas for resolving this, It was proved that is possible to determine the roots of high-order equations by using the same technique.



Sistemas dinâmicos não lineares, Método da expansão, Equações algébricas, Raízes de equações, Nonlinear dynamical systems, Expansion method, Algebraic equations, Roots of equations


HIROTA, Eduardo Koiti. Técnica de perturbação utilizada para solução numérica de equações do 2º e 3º graus. 2014. 64 f. Dissertação (Mestrado Profissional em Matemática em Rede Nacional) - Universidade Federal de Goiás, Catalão, 2014.