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

Juan Francisco Sánchez-Pérez (), Gonzalo García-Ros, Manuel Conesa, Enrique Castro and Manuel Cánovas
Additional contact information
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

Mathematics, 2023, vol. 11, issue 10, 1-28

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.

Keywords: nondimensionalization; universal solution; dimensionless groups; numerical simulation; differential equations; engineering problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/10/2303/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/10/2303/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:10:p:2303-:d:1147434

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().