The lower bound error as an auxiliary technique to select the integration step-size in the simulation of chaotic systems

Abstract

This work presents a method to choose the integration step-size h for discretization of nonlinear and chaotic dynamic systems, in order to obtain a simulation with numerical reliability. In this context, the Lower Bound Error is used as an auxiliary technique in the search for the optimal value of h, considering the Fourth Order Runge Kutta as the discretization method. The Lorenz equations, Rössler equations and Duffing-Ueda oscillator were used as case studies. This work, besides investigating the most adequate step-size h for each case, shows that the choice of very small values of h results in significantly inferior solutions, despite the consensus that the smaller the step-size, the higher the accuracy.