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Truncation Error of the Network Simulation Method: Chaotic Dynamical Systems in Mechanical Engineering

Author

Listed:
  • Joaquín Solano

    (Department of Mechanical Engineering, Materials and Manufacturing, Faculty of Industrial Engineering, Politechnic University of Cartagena, 30202 Cartagena, Spain
    These authors contributed equally to this work.)

  • Javier Mulas-Pérez

    (Department of Thermal and Fluid Engineering, Faculty of Industrial Engineering, Politechnic University of Cartagena, 30202 Cartagena, Spain
    These authors contributed equally to this work.)

  • Francisco Balibrea

    (Department of Mathematics, Faculty of Mathematics, University of Murcia, 30100 Murcia, Spain
    These authors contributed equally to this work.)

  • José Andrés Moreno-Nicolás

    (Department of Mechanical Engineering, Materials and Manufacturing, Faculty of Industrial Engineering, Politechnic University of Cartagena, 30202 Cartagena, Spain
    These authors contributed equally to this work.)

Abstract

This article focuses on the study of local truncation errors (LTEs) in the Network Simulation Method (NSM), specifically when using the trapezoidal method and Gear’s methods. The NSM, which represents differential equations through electrical circuit elements, offers advantages in solving nonlinear dynamic systems such as the van der Pol equation. The analysis compares the performance of these numerical methods in terms of their stability and error minimization, with particular emphasis on LTE. By leveraging circuit-based techniques prior to numerical application, the NSM improves convergence. This study evaluates the impact of step size on LTE and highlights the trade-offs between accuracy and computational cost when using the trapezoidal and Gear methods.

Suggested Citation

  • Joaquín Solano & Javier Mulas-Pérez & Francisco Balibrea & José Andrés Moreno-Nicolás, 2024. "Truncation Error of the Network Simulation Method: Chaotic Dynamical Systems in Mechanical Engineering," Mathematics, MDPI, vol. 12(21), pages 1-19, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:21:p:3441-:d:1513499
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    References listed on IDEAS

    as
    1. Joaquín Solano & Francisco Balibrea & José Andrés Moreno, 2021. "Applications of the Network Simulation Method to Differential Equations with Singularities and Chaotic Behaviour," Mathematics, MDPI, vol. 9(12), pages 1-12, June.
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