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 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.

• Autores: Acosta-Humánez, Primitivo Belén; Jiménez, M.; Ospino, Jorge
• 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
• License: Licencia de Creative Commons Reconocimiento-NoComercial-CompartirIgual 4.0 Internacional