RT info:eu-repo/semantics/article
T1 The Newton Polygon Method for Differential Equations
A1 Cano Torres, José María
K1 Matemáticas
K1 Newton polygon method
K1 Formal power series
K1 Ordinary differential equations
K1 1201 Álgebra
K1 1204 Geometría
AB We prove that a first order ordinary differential equation(ODE) with a dicritical singularity at the origin has a one-parameterfamily of convergent fractional power series solutions. The notion of adicritical singularity is extended from the class of first order and firstdegree ODE’s to the class of first order ODE’s. An analogous result forseries with real exponents is given.The main tool used in this paper is the Newton polygon methodfor ODE. We give a description of this method and some elementaryapplications such as an algorithm for finding polynomial solutions.
PB Springer Verlag
SN 0302-9743
YR 2005
FD 2005
LK https://uvadoc.uva.es/handle/10324/66227
UL https://uvadoc.uva.es/handle/10324/66227
LA spa
NO Cano, J. (2005). The Newton Polygon Method for Differential Equations. In: Li, H., Olver, P.J., Sommer, G. (eds) Computer Algebra and Geometric Algebra with Applications. IWMM GIAE 2004 2004. Lecture Notes in Computer Science, vol 3519. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11499251_3
NO Producción Científica
DS UVaDOC
RD 04-dic-2024