Existence and convergence of Puiseux series solutions for autonomous first order differential equations

DOI10.1016/j.jsc.2020.06.010zbMath1471.34026arXiv1908.09196OpenAlexW3037032005WikidataQ115345221 ScholiaQ115345221MaRDI QIDQ2048161

José Maria Cano, Sebastian Falkensteiner, Juan Rafael Sendra

Publication date: 5 August 2021

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.09196

zbMATH Keywords

algebraic differential equationalgebraic curveplaceconvergent solutionformal Puiseux series solution

Mathematics Subject Classification ID

Implicit ordinary differential equations, differential-algebraic equations (34A09) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25)

Related Items (4)

The algebro-geometric method: Solving algebraic differential equations by parametrizations ⋮ Algebraic and Puiseux series solutions of systems of autonomous algebraic ODEs of dimension one in several variables ⋮ The asymptotic solutions of two-term linear fractional differential equations via Laplace transform ⋮ On existence and uniqueness of formal power series solutions of algebraic ordinary differential equations

Cites Work

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• An extension of the Newton-Puiseux polygon construction to give solutions of Pfaffian forms
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• A polynomial time algorithm for finding rational general solutions of first order autonomous ODEs
• Solving Ordinary Differential Equations in Terms of Series with Real Exponents
• Rational general solutions of algebraic ordinary differential equations
• Algebraic general solutions of algebraic ordinary differential equations
• Computer Algebra and Geometric Algebra with Applications

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