Abstract
The approach we used earlier to construct Laurent and regular solutions enables one, in combination with the well-known Newton polygon algorithm, to find formal exponential-logarithmic solutions of linear ordinary differential equations the coefficients of which have the form of truncated power series. (Thus, only incomplete information about the original equation is available.) The series involved in the solution are also represented in truncated form. For these series, the combined approach proposed enables one to obtain the maximum possible number of terms.
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ACKNOWLEDGMENTS
We are grateful to Maplesoft (Waterloo, Canada) for consultations and discussions.
Funding
This work was supported by the Russian Foundation for Basic Research, project no. 19-01-00032.
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Translated by E. Chernokozhin
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Abramov, S.A., Ryabenko, A.A. & Khmelnov, D.E. Truncated Series and Formal Exponential-Logarithmic Solutions of Linear Ordinary Differential Equations. Comput. Math. and Math. Phys. 60, 1609–1620 (2020). https://doi.org/10.1134/S0965542520100024
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DOI: https://doi.org/10.1134/S0965542520100024