Solving transcendental equations of physics with Chebyshev's method

In this work, physics teachers are provided with an optimized method to solve transcendental equations that cannot be solved algebraically and appear very often in higher education physics and engineering courses. The method is based on an interpolation with Chebyshev’s polynomials, and it is optimi...

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Detalles Bibliográficos
Autor principal: Marqués Villarroya, David
Formato: Artículo revista
Lenguaje:Español
Publicado: Asociación de Profesores de Física de la Argentina 2022
Materias:
Transcendental equations
Chebyshev
Mathematics
Physics
Root-finder
Ecuaciones trascendentes
Raíces
Matemáticas
Física
Acceso en línea:https://revistas.unc.edu.ar/index.php/revistaEF/article/view/39487
Aporte de:
Revista de Enseñanza de la Física de Universidad Nacional de Córdoba
id I10-R316-article-39487
record_format ojs
spelling I10-R316-article-394872023-09-12T16:43:35Z Solving transcendental equations of physics with Chebyshev's method Resolución de ecuaciones trascendentes de la física mediante el método de Chebyshev Marqués Villarroya, David Transcendental equations Chebyshev Mathematics Physics Root-finder Ecuaciones trascendentes Chebyshev Raíces Matemáticas Física In this work, physics teachers are provided with an optimized method to solve transcendental equations that cannot be solved algebraically and appear very often in higher education physics and engineering courses. The method is based on an interpolation with Chebyshev’s polynomials, and it is optimized for computational time, manageability, and accuracy. The method has been applied in specific problems of physics where transcendental equations appear, such as the compression of a real spring; the equation of a diode; the solution of the Schrödinger equation in a potential well; and the computing of cutoff wave numbers of a coaxial wire. The method is compared with others of the literature to check its correct behavior and the improvements that it presents. MATLAB source codes to implement the method and particular examples are also provided. En este trabajo se proporciona a los docentes de física un método optimizado para resolver ecuaciones trascendentes que no pueden resolverse de manera algebraica y aparecen muy a menudo en cursos de enseñanza superior de física e ingeniería. El método se basa en una interpolación con polinomios de Chebyshev y está optimizado en tiempo computacional, facilidad de uso y precisión. El método se ha aplicado en problemas particulares de la física donde aparecen ecuaciones trascendentes como la compresión de un resorte real; la ecuación de un diodo; la solución de la ecuación de Schrödinger en un pozo de potencial; y el cálculo de números de onda de corte de un cable coaxial. Se compara el método con otros de la bibliografía para comprobar su correcto funcionamiento y las mejoras que presenta. También se proporcionan los códigos fuente de MATLAB para implementar el método y los ejemplos particulares. Asociación de Profesores de Física de la Argentina 2022-11-29 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion application/pdf text/html https://revistas.unc.edu.ar/index.php/revistaEF/article/view/39487 10.55767/2451.6007.v34.n2.39487 Journal of Physics Teaching; Vol. 34 No. 2 (2022): July - December; 97-108 Revista de Enseñanza de la Física; Vol. 34 Núm. 2 (2022): Julio - Diciembre; 97-108 Revista de Enseñanza de la Física; v. 34 n. 2 (2022): Julho - Dezembro; 97-108 2250-6101 0326-7091 10.55767/2451.6007.v34.n2 spa https://revistas.unc.edu.ar/index.php/revistaEF/article/view/39487/39457 https://revistas.unc.edu.ar/index.php/revistaEF/article/view/39487/39458 http://creativecommons.org/licenses/by-nc-nd/4.0
institution Universidad Nacional de Córdoba
institution_str I-10
repository_str R-316
container_title_str Revista de Enseñanza de la Física
language Español
format Artículo revista
topic Transcendental equations
Chebyshev
Mathematics
Physics
Root-finder
Ecuaciones trascendentes
Chebyshev
Raíces
Matemáticas
Física
spellingShingle Transcendental equations
Chebyshev
Mathematics
Physics
Root-finder
Ecuaciones trascendentes
Chebyshev
Raíces
Matemáticas
Física
Marqués Villarroya, David
Solving transcendental equations of physics with Chebyshev's method
topic_facet Transcendental equations
Chebyshev
Mathematics
Physics
Root-finder
Ecuaciones trascendentes
Chebyshev
Raíces
Matemáticas
Física
author Marqués Villarroya, David
author_facet Marqués Villarroya, David
author_sort Marqués Villarroya, David
title Solving transcendental equations of physics with Chebyshev's method
title_short Solving transcendental equations of physics with Chebyshev's method
title_full Solving transcendental equations of physics with Chebyshev's method
title_fullStr Solving transcendental equations of physics with Chebyshev's method
title_full_unstemmed Solving transcendental equations of physics with Chebyshev's method
title_sort solving transcendental equations of physics with chebyshev's method
description In this work, physics teachers are provided with an optimized method to solve transcendental equations that cannot be solved algebraically and appear very often in higher education physics and engineering courses. The method is based on an interpolation with Chebyshev’s polynomials, and it is optimized for computational time, manageability, and accuracy. The method has been applied in specific problems of physics where transcendental equations appear, such as the compression of a real spring; the equation of a diode; the solution of the Schrödinger equation in a potential well; and the computing of cutoff wave numbers of a coaxial wire. The method is compared with others of the literature to check its correct behavior and the improvements that it presents. MATLAB source codes to implement the method and particular examples are also provided.
publisher Asociación de Profesores de Física de la Argentina
publishDate 2022
url https://revistas.unc.edu.ar/index.php/revistaEF/article/view/39487
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first_indexed 2024-09-03T20:40:47Z
last_indexed 2024-09-03T20:40:47Z
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