Rational reparametrization of odes with radical coefficients
- J. RAFAEL SENDRA
- DAVID SEVILLA
- CARLOS VILLARINO
ISSN: 1132-6360
Ano de publicación: 2018
Título do exemplar: Proceedings of the XVI EACA Zaragoza Encuentros de Algebra Computacional y Aplicaciones
Número: 43
Páxinas: 135-138
Tipo: Artigo
Outras publicacións en: Monografías de la Real Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza
Resumo
Given an ordinary differential equation F(x, y(x), y0 (x), . . . , yn) (x)) = 0, polynomial in y, y0 , . . . , yn) and whose coefficients are complex radical expressions in x, we analyze whether there exists a rational change of variable x = r(z) such that the new differential equation G(z, Y (z), . . . , Y n) (z)) = 0 where Y (z) = y(r(z)) is algebraic (i.e. its coefficients are rational in z). We describe an algorithm for this purpose, which provides also the inverse transformation, so that the solutions of both ODEs are related. In the particular case y 0 (x) = δ(x) with δ(x) an algebraic radical expression in x, the algorithm outputs a change of variable into a rational integrand.