Estudo do efeito da variação no passo sobre o erro no método de runge-kutta de quarta ordem clássico

Abstract

Numerical methods for solving differential equations have widely permeated many fields of engineering, mostly due to their simplicity of computational implementation and efficiency to provide results. Among many methods available, the fourth-order Runge-Kutta method (RK4) stands out, being one of the most frequently used due to its high efficiency. The RK4 method, however, lacks simple ways to estimate the error, which would be useful in determining the step to be adopted. In this context, the present work studies how the step variation in the RK4 method affects its respective error. This study was carried out with problems adapted from the classical literature of Strength of Materials addressing isostatic beams subjected to different external loads. It has been found in one of the IVP's that as the step is reduced, the error is also reduced, following a relationship governed by a power function. For the other cases, an error of very low magnitude was observed, remaining approximately constant.