The Newton method for plane algebraic curves is based on the following remark: the first term of a series, root of a polynomial with coefficients in the ring of series in one variable, is a solution of an initial equation that can be determined by the Newton polygon. Given a monomial ordering in the ring of polynomials in several variables, we describe the systems of initial equations that satisfy the first terms of the solutions of a system of partial differential equations. As a consequence, we extend Mora and Robbiano’s Groebner fan to differential ideals.
Newton's lemma for differential equations / Aroca, Fuensanta; Ilardi, Giovanna. - In: ILLINOIS JOURNAL OF MATHEMATICS. - ISSN 0019-2082. - 60:3-4(2016), pp. 859-867.
Newton's lemma for differential equations
ILARDI, GIOVANNA
2016
Abstract
The Newton method for plane algebraic curves is based on the following remark: the first term of a series, root of a polynomial with coefficients in the ring of series in one variable, is a solution of an initial equation that can be determined by the Newton polygon. Given a monomial ordering in the ring of polynomials in several variables, we describe the systems of initial equations that satisfy the first terms of the solutions of a system of partial differential equations. As a consequence, we extend Mora and Robbiano’s Groebner fan to differential ideals.File | Dimensione | Formato | |
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