Galoisian and numerical approach of three dimensional linear differential systems with skew symmetric matrices defined in a non- constant differential field
This work contrasts numerical methods with algebraic methods. These methods are applied to solve a three dimensional linear differential system with skew symmetric matrices defined in a non- constant differential field. Algorithms and methods of Differential Galois Theory, are used to provide an alg...
- Autores:
-
Acosta-Humánez, Primitivo Belén
Jiménez, M.
Ospino, Jorge
- Tipo de recurso:
- Fecha de publicación:
- 2018
- Institución:
- Universidad Simón Bolívar
- Repositorio:
- Repositorio Digital USB
- Idioma:
- spa
- OAI Identifier:
- oai:bonga.unisimon.edu.co:20.500.12442/1935
- Acceso en línea:
- http://hdl.handle.net/20.500.12442/1935
- Palabra clave:
- Differential Galois theory
Methods from Runge - Kutta family
Liouvillians solutions
Differential system of equations
Skew symmetric matrices
Non-constant differential field
Teoría de Galois diferencial
Métodos de la familia de Runge - Kutta
Soluciones Liouvillianas
Sistemas de ecuaciones diferenciales
Matrices antisimétricas
Cuerpo diferencial no constante
- Rights
- License
- Licencia de Creative Commons Reconocimiento-NoComercial-CompartirIgual 4.0 Internacional
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| dc.title.eng.fl_str_mv |
Galoisian and numerical approach of three dimensional linear differential systems with skew symmetric matrices defined in a non- constant differential field |
| title |
Galoisian and numerical approach of three dimensional linear differential systems with skew symmetric matrices defined in a non- constant differential field |
| spellingShingle |
Galoisian and numerical approach of three dimensional linear differential systems with skew symmetric matrices defined in a non- constant differential field Differential Galois theory Methods from Runge - Kutta family Liouvillians solutions Differential system of equations Skew symmetric matrices Non-constant differential field Teoría de Galois diferencial Métodos de la familia de Runge - Kutta Soluciones Liouvillianas Sistemas de ecuaciones diferenciales Matrices antisimétricas Cuerpo diferencial no constante |
| title_short |
Galoisian and numerical approach of three dimensional linear differential systems with skew symmetric matrices defined in a non- constant differential field |
| title_full |
Galoisian and numerical approach of three dimensional linear differential systems with skew symmetric matrices defined in a non- constant differential field |
| title_fullStr |
Galoisian and numerical approach of three dimensional linear differential systems with skew symmetric matrices defined in a non- constant differential field |
| title_full_unstemmed |
Galoisian and numerical approach of three dimensional linear differential systems with skew symmetric matrices defined in a non- constant differential field |
| title_sort |
Galoisian and numerical approach of three dimensional linear differential systems with skew symmetric matrices defined in a non- constant differential field |
| dc.creator.fl_str_mv |
Acosta-Humánez, Primitivo Belén Jiménez, M. Ospino, Jorge |
| dc.contributor.author.none.fl_str_mv |
Acosta-Humánez, Primitivo Belén Jiménez, M. Ospino, Jorge |
| dc.subject.eng.fl_str_mv |
Differential Galois theory Methods from Runge - Kutta family Liouvillians solutions Differential system of equations Skew symmetric matrices Non-constant differential field |
| topic |
Differential Galois theory Methods from Runge - Kutta family Liouvillians solutions Differential system of equations Skew symmetric matrices Non-constant differential field Teoría de Galois diferencial Métodos de la familia de Runge - Kutta Soluciones Liouvillianas Sistemas de ecuaciones diferenciales Matrices antisimétricas Cuerpo diferencial no constante |
| dc.subject.spa.fl_str_mv |
Teoría de Galois diferencial Métodos de la familia de Runge - Kutta Soluciones Liouvillianas Sistemas de ecuaciones diferenciales Matrices antisimétricas Cuerpo diferencial no constante |
| description |
This work contrasts numerical methods with algebraic methods. These methods are applied to solve a three dimensional linear differential system with skew symmetric matrices defined in a non- constant differential field. Algorithms and methods of Differential Galois Theory, are used to provide an algebraic solution, while numerical methods, in particular, methods from Runge - Kutta family, are applied to the same system. Finally, the absolute and relative errors between Liouvillians solution are calculated comparing the solutions obtained by means of algebraic methods and by means of numerical methods. |
| publishDate |
2018 |
| dc.date.accessioned.none.fl_str_mv |
2018-04-02T21:46:18Z |
| dc.date.available.none.fl_str_mv |
2018-04-02T21:46:18Z |
| dc.date.issued.none.fl_str_mv |
2018-01 |
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article |
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http://purl.org/coar/resource_type/c_6501 |
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02131315 |
| dc.identifier.uri.none.fl_str_mv |
http://hdl.handle.net/20.500.12442/1935 |
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02131315 |
| url |
http://hdl.handle.net/20.500.12442/1935 |
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spa |
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spa |
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http://purl.org/coar/access_right/c_abf2 |
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Licencia de Creative Commons Reconocimiento-NoComercial-CompartirIgual 4.0 Internacional |
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Licencia de Creative Commons Reconocimiento-NoComercial-CompartirIgual 4.0 Internacional http://purl.org/coar/access_right/c_abf2 |
| dc.publisher.spa.fl_str_mv |
Editorial board |
| dc.source.spa.fl_str_mv |
Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería Vol. 34, No.1 (2018) |
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Universidad Simón Bolívar |
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https://www.scipedia.com/public/Acosta-Hum%C3%A1nez_et_al_2017a# |
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Licencia de Creative Commons Reconocimiento-NoComercial-CompartirIgual 4.0 Internacionalhttp://purl.org/coar/access_right/c_abf2Acosta-Humánez, Primitivo Belén94d27213-2a81-4a82-b710-e58036779ab7-1Jiménez, M.ead0ceca-acd6-4234-9e11-d920ae50194b-1Ospino, Jorge08596f1e-e939-4bf9-bb00-f9c947ab22f6-12018-04-02T21:46:18Z2018-04-02T21:46:18Z2018-0102131315http://hdl.handle.net/20.500.12442/1935This work contrasts numerical methods with algebraic methods. These methods are applied to solve a three dimensional linear differential system with skew symmetric matrices defined in a non- constant differential field. Algorithms and methods of Differential Galois Theory, are used to provide an algebraic solution, while numerical methods, in particular, methods from Runge - Kutta family, are applied to the same system. Finally, the absolute and relative errors between Liouvillians solution are calculated comparing the solutions obtained by means of algebraic methods and by means of numerical methods.Este trabajo contrasta métodos numéricos con métodos algebraicos aplicados ambos a la resolución de un sistema de ecuaciones diferenciales lineales 3-dimensionales con matrices antisimétricas definidas en un cuerpo diferencial no constante. Al mismo sistema se aplican métodos y algorítmos propios de la Teoría de Galois Diferencial, lo que permite resolverlo algebraicamente y métodos numéricos, en particular métodos de la familia de Runge - Kutta. Por último, se calculan los errores absolutos y relativos entre las soluciones Liouvillianas, obtenidas mediante la resolución algebraica y las soluciones obtenidas aplicando métodos numéricos.spaEditorial boardRevista Internacional de Métodos Numéricos para Cálculo y Diseño en IngenieríaVol. 34, No.1 (2018)https://www.scipedia.com/public/Acosta-Hum%C3%A1nez_et_al_2017a#Differential Galois theoryMethods from Runge - Kutta familyLiouvillians solutionsDifferential system of equationsSkew symmetric matricesNon-constant differential fieldTeoría de Galois diferencialMétodos de la familia de Runge - KuttaSoluciones LiouvillianasSistemas de ecuaciones diferencialesMatrices antisimétricasCuerpo diferencial no constanteGaloisian and numerical approach of three dimensional linear differential systems with skew symmetric matrices defined in a non- constant differential fieldarticlehttp://purl.org/coar/resource_type/c_6501P.B. Acosta-Humánez, Galoisian Approach to Supersymmetric Quantum Mechanics. PhD. Thesis, Technical University of Catalonia, abril 2009.P. B. Acosta-Humánez, E. Suazo, Liouvillian propagators, Riccati equation and diferential theory. Journal of Physics a: Mathematical and Theoretical, 46, 2013.P. B. Acosta-Humánez, M. Machado, A. V. Sinitsyn A model of anaerobic digestion for biogas production using Abel equations. Far East Journal of Mathematical Sciences (FJMS), 101:1295-1311, 2017.R. Bulirsch, J. Stoer, Introduction to numerical analisys. Third edition. Springer-Verlag, 2002.J. C. Butcher, Numerical methods for ordinary differential equations. John Wiley and Sons, Second edition, 2008.J. D. Lambert, Numerical methods for Ordinary differential sistems. The initial value problem. John Wiley and Sons, 1991.Matlab. Available: http://www.mathworks.comJ. J. Morales-Ruiz, Differential Galois Theory and non-integrability of Hamiltonian systems. Birkhaüser, 1999.P.B. Acosta-Humánez, La teoría de Morales-Ramis y el algoritmo de Kovacic. Lecturas Matemáticas, Volumen Especial, pp. 21-56, 2006.R. L. Burden, J. Douglas Faires, Análisis numérico. Cengage Learning, Séptima edición, 2009.M. Calvo, J. I. Montijano, L. Rández, Una familia de métodos multirevolución Runge-Kutta explícitos de orden cinco. Departamento Matemática Aplicada, Universidad de Zaragoza, pp. 45-54, 2003.A. Campos, Cómo obtener ecuaciones reducidas de Riccati invariantes con respecto a un campo de vectores. Lecturas Matemáticas, Volumen Especial, pp. 95-103, 2006.S. A. Carrillo Torres, Constructibilidad mediante funciones Liouvillianas de curvas espaciales con curvatura y torsión racionales. Trabajo de grado, Universidad Sergio Arboleda, 2009.W, Cheney, D, Kincaid, Métodos numéricos y computación. Cengage Learning, Sexta edición, 2011.M. I. Jiménez Niebles, Enfoque Galoisiano y numérico de sistemas diferenciales lineales 3-dimensionales con matrices antisimétricas definidas en un cuerpo diferencial no constante. Tésis de Maestría, Universidad del Norte, 2015.T. Sauer, Análisis numérico. Pearson, Segunda edición, 2013.LICENSElicense.txtlicense.txttext/plain; charset=utf-8368https://bonga.unisimon.edu.co/bitstreams/8e5a20c9-63e1-4a51-a494-0703c0f905ca/download3fdc7b41651299350522650338f5754dMD5220.500.12442/1935oai:bonga.unisimon.edu.co:20.500.12442/19352019-04-11 21:51:35.268metadata.onlyhttps://bonga.unisimon.edu.coDSpace UniSimonbibliotecas@biteca.comPGEgcmVsPSJsaWNlbnNlIiBocmVmPSJodHRwOi8vY3JlYXRpdmVjb21tb25zLm9yZy9saWNlbnNlcy9ieS1uYy80LjAvIj48aW1nIGFsdD0iTGljZW5jaWEgQ3JlYXRpdmUgQ29tbW9ucyIgc3R5bGU9ImJvcmRlci13aWR0aDowIiBzcmM9Imh0dHBzOi8vaS5jcmVhdGl2ZWNvbW1vbnMub3JnL2wvYnktbmMvNC4wLzg4eDMxLnBuZyIgLz48L2E+PGJyLz5Fc3RhIG9icmEgZXN0w6EgYmFqbyB1bmEgPGEgcmVsPSJsaWNlbnNlIiBocmVmPSJodHRwOi8vY3JlYXRpdmVjb21tb25zLm9yZy9saWNlbnNlcy9ieS1uYy80LjAvIj5MaWNlbmNpYSBDcmVhdGl2ZSBDb21tb25zIEF0cmlidWNpw7NuLU5vQ29tZXJjaWFsIDQuMCBJbnRlcm5hY2lvbmFsPC9hPi4= |