Rational reparametrization of odes with radical coefficients
- J. RAFAEL SENDRA
- DAVID SEVILLA
- CARLOS VILLARINO
ISSN: 1132-6360
Argitalpen urtea: 2018
Zenbakien izenburua: Proceedings of the XVI EACA Zaragoza Encuentros de Algebra Computacional y Aplicaciones
Zenbakia: 43
Orrialdeak: 135-138
Mota: Artikulua
Beste argitalpen batzuk: Monografías de la Real Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza
Laburpena
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.