Comparison of computational numerical methods in an initial value problem solution

Abstract

Ordinary differential equations (ODE) occur very often in the description of nature phenomena. There are several methods that analytically solving an ODE, however it is not always possible to obtain this solution. In this case, numerical methods are used to find an approximate solution. In this paper discusses the development and the use of two numerical methods for ODE's resolution. For this we will concentrate primarily in initial value problems for first order equations. In this context, we will treat the comparison of two computational numerical methods used to approximate ordinary differential equations, given an initial value problem (IVP) and the related analytical solution of the equation. The first method is the 2nd order Taylor and the second is 3rd order Runge-Kutta. The main objective is to implement the two numerical methods in MatLab software and analyze if they approach of the exact solution. With the results obtained, must conclude which of the two methods is more effective for this type of problem.