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The novel family of transcendental Leal-functions with applications to science and engineering

During the phenomena modelling process in the different areas of science and engineering is common to face nonlinear equations without exact solutions; thus, the need of employing numerical methods to obtain such solutions. Therefore, in order to provide new possibilities for the isolation of variab...

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Autores principales: Vazquez-Leal, Hector, Sandoval-Hernandez, Mario Alberto, Filobello-Nino, Uriel
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Elsevier 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7666359/
https://www.ncbi.nlm.nih.gov/pubmed/33225088
http://dx.doi.org/10.1016/j.heliyon.2020.e05418
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author Vazquez-Leal, Hector
Sandoval-Hernandez, Mario Alberto
Filobello-Nino, Uriel
author_facet Vazquez-Leal, Hector
Sandoval-Hernandez, Mario Alberto
Filobello-Nino, Uriel
author_sort Vazquez-Leal, Hector
collection PubMed
description During the phenomena modelling process in the different areas of science and engineering is common to face nonlinear equations without exact solutions; thus, the need of employing numerical methods to obtain such solutions. Therefore, in order to provide new possibilities for the isolation of variables, we propose a novel family of transcendental functions with new algebraic properties including their integration and differentiation rules. Likewise, in order facilitate the numerical evaluation for every new family set of functions, a highly accurate series of approximations is proposed by employing analytical expressions in terms of known transcendental functions and polynomials combinations. By the use of known functions for the proposed approximations, makes possible the use of any programming language for their respective implementation. In this article, three interesting case studies are presented with applications on: coastal engineering, transmission lines span on electrical engineering, and the planar one-dimensional Bratu equation. Finally, based on the results from study cases, it can be concluded that Leal-functions will have relevant impact in all areas of physics and mathematics, by providing new tools to scientists and engineers for the proposal of new mathematical models and numerical/analytical analysis, design and implementation of new theories and technological innovations.
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spelling pubmed-76663592020-11-20 The novel family of transcendental Leal-functions with applications to science and engineering Vazquez-Leal, Hector Sandoval-Hernandez, Mario Alberto Filobello-Nino, Uriel Heliyon Research Article During the phenomena modelling process in the different areas of science and engineering is common to face nonlinear equations without exact solutions; thus, the need of employing numerical methods to obtain such solutions. Therefore, in order to provide new possibilities for the isolation of variables, we propose a novel family of transcendental functions with new algebraic properties including their integration and differentiation rules. Likewise, in order facilitate the numerical evaluation for every new family set of functions, a highly accurate series of approximations is proposed by employing analytical expressions in terms of known transcendental functions and polynomials combinations. By the use of known functions for the proposed approximations, makes possible the use of any programming language for their respective implementation. In this article, three interesting case studies are presented with applications on: coastal engineering, transmission lines span on electrical engineering, and the planar one-dimensional Bratu equation. Finally, based on the results from study cases, it can be concluded that Leal-functions will have relevant impact in all areas of physics and mathematics, by providing new tools to scientists and engineers for the proposal of new mathematical models and numerical/analytical analysis, design and implementation of new theories and technological innovations. Elsevier 2020-11-09 /pmc/articles/PMC7666359/ /pubmed/33225088 http://dx.doi.org/10.1016/j.heliyon.2020.e05418 Text en © 2020 The Authors http://creativecommons.org/licenses/by/4.0/ This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Research Article
Vazquez-Leal, Hector
Sandoval-Hernandez, Mario Alberto
Filobello-Nino, Uriel
The novel family of transcendental Leal-functions with applications to science and engineering
title The novel family of transcendental Leal-functions with applications to science and engineering
title_full The novel family of transcendental Leal-functions with applications to science and engineering
title_fullStr The novel family of transcendental Leal-functions with applications to science and engineering
title_full_unstemmed The novel family of transcendental Leal-functions with applications to science and engineering
title_short The novel family of transcendental Leal-functions with applications to science and engineering
title_sort novel family of transcendental leal-functions with applications to science and engineering
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7666359/
https://www.ncbi.nlm.nih.gov/pubmed/33225088
http://dx.doi.org/10.1016/j.heliyon.2020.e05418
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