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JOURNALS // Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia // Archive

Dokl. RAN. Math. Inf. Proc. Upr., 2022 Volume 503, Pages 70–75 (Mi danma253)

MATHEMATICS

On convergent series expansions for solutions of nonlinear ordinary differential equations

V. S. Samovol

National Research University "Higher School of Economics", Moscow, Russia

Abstract: We consider a large class of nonlinear ordinary differential equations of arbitrary order with coefficients in the form of power series that converge in a neighborhood of the origin. There are known power-geometry methods and algorithms based on them for the computation of power-logarithmic series (Dulac series) that formally satisfy such equations. We prove a sufficient condition for the convergence of such formal solutions.

Keywords: Newton polygon, continuable solution, formal solution, Dulac series, convergence.

UDC: 517.922

Presented: B. N. Chetverushkin
Received: 18.04.2021
Revised: 28.12.2021
Accepted: 21.01.2022

DOI: 10.31857/S2686954322020151


 English version:
Doklady Mathematics, 2022, 105:2, 112–116

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© Steklov Math. Inst. of RAS, 2026