Método de Euler para resolução de equações diferenciais ordinárias

Abstract

The present work aims to employ the Euler’s method in the approximation of solutions of ordinary differential equations with initial value problem, as well as to introduce some concepts of differential equations and describe the Euler’s method. This work was carried out by bibliographic review through books, monographs, articles and theses of master's and doctorate. Euler's method uses the concept of tangent curve to find the results and one of the solutions to the problem, that is, a point in the solution curve, to find the next one. And by using a tangente line, it is to be expected that the value found will not be equal to the exact solution. In this sense, in the course of this work are found theorems related to the existence and uniqueness of differential equations, as well as improvements to the Euler’s method. At the end of this study it was concluded that the Euler’s method and its improvements can achieve a good approximation for the solutions of problems of initial value, considering the consistency of the problem in question and the errors generated during the calculations