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Methodology to Obtain Universal Solutions for Systems of Coupled Ordinary Differential Equations: Examples of a Continuous Flow Chemical Reactor and a Coupled Oscillator

Author

Listed:
  • Juan Francisco Sánchez-Pérez

    (Department of Applied Physics and Naval Technology, Universidad Politécnica de Cartagena (UPCT), 30202 Cartagena, Spain)

  • Gonzalo García-Ros

    (Department of Mining and Civil Engineering, Universidad Politécnica de Cartagena (UPCT), 30202 Cartagena, Spain)

  • Manuel Conesa

    (Department of Applied Physics and Naval Technology, Universidad Politécnica de Cartagena (UPCT), 30202 Cartagena, Spain)

  • Enrique Castro

    (Department of Applied Physics and Naval Technology, Universidad Politécnica de Cartagena (UPCT), 30202 Cartagena, Spain)

  • Manuel Cánovas

    (Metallurgical and Mining Engineering Department, Universidad Católica del Norte, Antofagasta 1240000, Chile)

Abstract

This paper presents a concise and orderly methodology to obtain universal solutions to different problems in science and engineering using the nondimensionalization of the governing equations of the physical–chemical problem posed. For its application, a deep knowledge of the problem is necessary since it will facilitate the adequate choice of the references necessary for its resolution. In addition, the application of the methodology to examples of coupled ordinary differential equations is shown, resulting in an interesting tool to teach postgraduate students in the branches of physics, mathematics, and engineering. The first example used for a system of coupled ordinary differential equations is a model of a continuous flow chemical reactor, where it is worth noting; on the one hand, the methodology used to choose the reference (characteristic) time and, on the other, the equivalence between the characteristic times obtained for each one of the species. The following universal curves are obtained, which are validated by comparing them with the results obtained by numerical simulation, where it stands out that the universal solution includes an unknown that must be previously obtained. The resolution of this unknown implies having a deep knowledge of the problem, a common characteristic when using the methodology proposed in this work for different engineering or physicochemical problems. Finally, the second example is a coupled oscillator, where it is worth noting that the appearance of characteristic periods that implicitly or explicitly affect the particles’ movement is striking.

Suggested Citation

  • Juan Francisco Sánchez-Pérez & Gonzalo García-Ros & Manuel Conesa & Enrique Castro & Manuel Cánovas, 2023. "Methodology to Obtain Universal Solutions for Systems of Coupled Ordinary Differential Equations: Examples of a Continuous Flow Chemical Reactor and a Coupled Oscillator," Mathematics, MDPI, vol. 11(10), pages 1-28, May.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2303-:d:1147434
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    References listed on IDEAS

    as
    1. Francisco Campuzano-Bolarín & Fulgencio Marín-García & José Andrés Moreno-Nicolás & Marija Bogataj & David Bogataj, 2021. "Network Simulation Method for the evaluation of perturbed supply chains on a finite horizon," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(3), pages 823-839, September.
    2. Gonzalo García-Ros & Iván Alhama & Manuel Cánovas & Francisco Alhama, 2018. "Derivation of Universal Curves for Nonlinear Soil Consolidation with Potential Constitutive Dependences," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-15, December.
    3. Gonzalo García-Ros & Iván Alhama, 2020. "Method to Determine the Constitutive Permeability Parameters of Non-Linear Consolidation Models by Means of the Oedometer Test," Mathematics, MDPI, vol. 8(12), pages 1-18, December.
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    Citations

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    Cited by:

    1. Manuel Conesa & Juan Francisco Sánchez-Pérez & Gonzalo García-Ros & Enrique Castro & Julio Valenzuela, 2023. "Normalization Method as a Potent Tool for Grasping Linear and Nonlinear Systems in Physics and Soil Mechanics," Mathematics, MDPI, vol. 11(20), pages 1-19, October.
    2. Juan Francisco Sánchez-Pérez & Guillermo Jorde-Cerezo & Adrián Fernández-Roiz & José Andrés Moreno-Nicolás, 2023. "Mathematical Modeling and Analysis Using Nondimensionalization Technique of the Solidification of a Splat of Variable Section," Mathematics, MDPI, vol. 11(14), pages 1-16, July.
    3. Juan Francisco Sánchez-Pérez & Santiago Oviedo-Casado & Gonzalo García-Ros & Manuel Conesa & Enrique Castro, 2024. "Understanding Complex Traffic Dynamics with the Nondimensionalisation Technique," Mathematics, MDPI, vol. 12(4), pages 1-14, February.

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