Nonlinear equations in Physics, and their resolution using high order multi-step iterative methods
This work provides the physics teacher with theoretical and computational foundations to solve nonlinear equations, very com-mon in solving physical problems. In the present research three physics problems are solved, which are: a sphere floating in water, non-free fall of a parachutist, compression...
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| Lenguaje: | Español Portugués |
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Asociación de Profesores de Física de la Argentina
2021
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| Acceso en línea: | https://revistas.unc.edu.ar/index.php/revistaEF/article/view/36000 |
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I10-R316-article-360002023-09-12T16:46:43Z Nonlinear equations in Physics, and their resolution using high order multi-step iterative methods Ecuaciones no lineales en física y su resolución mediante el uso de métodos iterativos multipaso de orden alto Quinga, Santiago Nonlinear equations Iterative multi-step methods Newton Ostrowski’s method Physics Ecuaciones no lineales Métodos iterativos multipaso Newton Métodos de Ostrowski Física This work provides the physics teacher with theoretical and computational foundations to solve nonlinear equations, very com-mon in solving physical problems. In the present research three physics problems are solved, which are: a sphere floating in water, non-free fall of a parachutist, compression of a real spring; making use of principles related to fluids, kinematics and dynamics. Nonlinear equations are obtained which are difficult and, in some cases, impossible to be solved by means of analyti-cal methods. To find an approximate solution to these equations we use iterative methods starting from traditional methods such as Newton, Secant, Steffensen to the introduction of multi-step methods with high order of convergence such as Traub, Ostrowski and methods of order eight designed from Ostrowski's method. Finally, an analysis of the results obtained by applying all these methods to each of the selected physical problems is carried out and, in this way, establish which iterative method is more appropriate in each situation. El presente trabajo proporciona al docente de física fundamentos teóricos y computacionales para resolver ecuaciones no linea-les, muy comunes en la solución de problemas físicos. En el presente trabajo de investigación se resuelven tres problemas de física, los cuales son: una esfera flotando en agua, caída no libre de un paracaidista, compresión de un resorte real; haciendo uso de principios referentes a fluidos, cinemática y dinámica. Se obtienen ecuaciones no lineales difíciles y en algunos casos imposi-bles de ser resueltas mediante métodos analíticos. Para encontrar una solución aproximada a dichas ecuaciones se hace uso de métodos iterativos partiendo desde los métodos tradicionales como son Newton, Secante, Steffensen hasta la introducción de métodos multipaso con alto orden de convergencia como son Traub, Ostrowski y métodos de orden ocho diseñados a partir del método de Ostrowski. Finalmente, se realiza un análisis de los resultados obtenidos al aplicar todos estos métodos a cada uno de los problemas físicos seleccionados y de esta formar establecer qué método iterativo es más adecuado ante cada situación. Asociación de Profesores de Física de la Argentina 2021-12-12 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion application/pdf text/html https://revistas.unc.edu.ar/index.php/revistaEF/article/view/36000 10.55767/2451.6007.v33.n3.36000 Journal of Physics Teaching; Vol. 33 No. 3 (2021): July - December; 145-165 Revista de Enseñanza de la Física; Vol. 33 Núm. 3 (2021): Julio - Diciembre; 145-165 Revista de Enseñanza de la Física; v. 33 n. 3 (2021): Julho - Dezembro; 145-165 2250-6101 0326-7091 spa por https://revistas.unc.edu.ar/index.php/revistaEF/article/view/36000/36142 https://revistas.unc.edu.ar/index.php/revistaEF/article/view/36000/36143 Derechos de autor 2021 Santiago Quinga 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 Portugués |
| format |
Artículo revista |
| topic |
Nonlinear equations Iterative multi-step methods Newton Ostrowski’s method Physics Ecuaciones no lineales Métodos iterativos multipaso Newton Métodos de Ostrowski Física |
| spellingShingle |
Nonlinear equations Iterative multi-step methods Newton Ostrowski’s method Physics Ecuaciones no lineales Métodos iterativos multipaso Newton Métodos de Ostrowski Física Quinga, Santiago Nonlinear equations in Physics, and their resolution using high order multi-step iterative methods |
| topic_facet |
Nonlinear equations Iterative multi-step methods Newton Ostrowski’s method Physics Ecuaciones no lineales Métodos iterativos multipaso Newton Métodos de Ostrowski Física |
| author |
Quinga, Santiago |
| author_facet |
Quinga, Santiago |
| author_sort |
Quinga, Santiago |
| title |
Nonlinear equations in Physics, and their resolution using high order multi-step iterative methods |
| title_short |
Nonlinear equations in Physics, and their resolution using high order multi-step iterative methods |
| title_full |
Nonlinear equations in Physics, and their resolution using high order multi-step iterative methods |
| title_fullStr |
Nonlinear equations in Physics, and their resolution using high order multi-step iterative methods |
| title_full_unstemmed |
Nonlinear equations in Physics, and their resolution using high order multi-step iterative methods |
| title_sort |
nonlinear equations in physics, and their resolution using high order multi-step iterative methods |
| description |
This work provides the physics teacher with theoretical and computational foundations to solve nonlinear equations, very com-mon in solving physical problems. In the present research three physics problems are solved, which are: a sphere floating in water, non-free fall of a parachutist, compression of a real spring; making use of principles related to fluids, kinematics and dynamics. Nonlinear equations are obtained which are difficult and, in some cases, impossible to be solved by means of analyti-cal methods. To find an approximate solution to these equations we use iterative methods starting from traditional methods such as Newton, Secant, Steffensen to the introduction of multi-step methods with high order of convergence such as Traub, Ostrowski and methods of order eight designed from Ostrowski's method. Finally, an analysis of the results obtained by applying all these methods to each of the selected physical problems is carried out and, in this way, establish which iterative method is more appropriate in each situation. |
| publisher |
Asociación de Profesores de Física de la Argentina |
| publishDate |
2021 |
| url |
https://revistas.unc.edu.ar/index.php/revistaEF/article/view/36000 |
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