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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2020 Volume 60, Number 1, Pages 4–17 (Mi zvmmf11010)

This article is cited in 14 papers

Regular solutions of linear ordinary differential equations and truncated series

S. A. Abramov, A. A. Ryabenko, D. E. Khmelnov

Dorodnitsyn Computing Center, Russian Academy of Sciences, Moscow, 119333 Russia

Abstract: Linear ordinary differential equations with coefficients in the form of truncated formal power series are considered. Earlier, it was discussed what can be found from an equation specified in this way about its solutions belonging to the field of formal Laurent series. Now a similar question is discussed for regular solutions. We are still interested in information about these solutions that is invariant under possible prolongations of truncated series representing the coefficients of the equation. The possibility of including in the solutions symbolic unspecified coefficients of possible prolongations of the equation is also considered.

Key words: computer algebra, differential equations, power series, truncated series, regular solutions.

UDC: 517.91

Received: 20.08.2019
Revised: 30.08.2019
Accepted: 18.09.2019

DOI: 10.31857/S0044466920010020


 English version:
Computational Mathematics and Mathematical Physics, 2020, 60:1, 1–14

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© Steklov Math. Inst. of RAS, 2025