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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...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Elsevier
2020
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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. |
format | Online Article Text |
id | pubmed-7666359 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
publisher | Elsevier |
record_format | MEDLINE/PubMed |
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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