The Lower Bound Error as an Auxiliary Technique to Select the Integration Step-size in the Simulation of Chaotic Systems

The code files used to get the results published in the paper "The Lower Bound Error as an Auxiliary Technique to Select the Integration Step-size in the Simulation of Chaotic Systems".

Download the manuscript here.

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.

Authors: Wilson Rocha Lacerda Junior, Samir Angelo Milani Martins e Erivelton Geraldo Nepomuceno.

Website: http://www.ufsj.edu.br/gcom

Please send suggestions for improvement of the above code to Wilson Rocha at this email address: wilsonrljr@outlook.com

References:

@ARTICLE{lacerdajunioretal2018,
  AUTHOR =       {Wilson Rocha {Lacerda Junior} and Samir Angelo Milani Martins and Erivelton Geraldo Nepomuceno},
  TITLE =        {The Lower Bound Error as an Auxiliary Technique to Select the Integration Step-Size in the Simulation of Chaotic Systems},
  JOURNAL =      {Learning \& Nonlinear Models},
  pages =        {56-67},
  publisher =    {ABRICOM},
  YEAR =         {2018},
  VOLUME =       {16},
  number =       {1},
}