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

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.

 Funding Agency Grant Number Russian Foundation for Basic Research 19-01-00032 This work was supported by the Russian Foundation for Basic Research (project no. 19-01-00032).

DOI: https://doi.org/10.31857/S0044466920010020

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

Bibliographic databases:

UDC: 517.91
Revised: 30.08.2019
Accepted:18.09.2019

Citation: S. A. Abramov, A. A. Ryabenko, D. E. Khmelnov, “Regular solutions of linear ordinary differential equations and truncated series”, Zh. Vychisl. Mat. Mat. Fiz., 60:1 (2020), 4–17; Comput. Math. Math. Phys., 60:1 (2020), 1–14

Citation in format AMSBIB
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