Comparative Analysis of Numerical Solutions of ODEs with Initial Value Problems using Improved Euler Methods.

This document contains a detailed comparison between the initial numerical solution methods of ordinary differential equations, which start from the Euler method approach, which is based on the solution of differential equations by the Taylor method, the others two methods to be compared are improvements of this method, that of Euler, and they are the method of Heun, and the method of the midpoint. It will be observed from the solution of test differential equations its respective error with respect to the analytical solution, obtaining an error index dictated by the mean square error EMC. Through this document we will know the best numerical approximation to the analytical solution of the different PVI (initial value problems) raised, also fixing a solution pattern for certain problems, that is, the appropriate method for each type of problem will be stipulated. [ABSTRACT FROM AUTHOR]