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Applications of the Network Simulation Method to Differential Equations with Singularities and Chaotic Behaviour

Author

Listed:
  • Joaquín Solano

    (Department of Automation, Electrical Engineering and Electronic Technology, Faculty of Industrial Engineering, Politechnic University of Cartagena (UPCT), 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

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

Abstract

In this paper, we deal with some applications of the network simulation method (NMS) to the non-linear differential equations derived of a parametric family associated to stated problems by Newton in and others like the parabolic mirror and van der Pol non-linear equation. We underly the efficientcy of the (NMS) method, compare it with Matlab procedures and present figures of solutions of the equations obtained by it on the mentioned problems. Additionally, we introduce also the electric-electronic circuits we have designed to be able of obtaining the solutions of the referred equations.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1442-:d:578706
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    Citations

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    Cited by:

    1. 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.
    2. Iván Alhama & José Antonio Jiménez-Valera & Manuel Cánovas & Francisco Alhama, 2024. "Deduction of the Dimensionless Groups and Type Curves of Temperature Profiles in Two-Layer Soils with Water Flow at Depth," Mathematics, MDPI, vol. 12(2), pages 1-16, January.

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