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On Truncated Series Involved in Exponential-Logarithmic Solutions of Truncated LODEs

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Computer Algebra in Scientific Computing (CASC 2022)

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Abstract

Previously, the authors proposed algorithms for finding exponential-logarithmic solutions of linear ordinary differential equations with coefficients in the form of series, for which only a finite number of initial terms is known. Each solution involves a finite set of power series, for which the maximum possible number of terms is calculated. Below, these algorithms are supplemented with the option to confirm the impossibility of obtaining a larger number of terms in the series without using additional information about the given equation. Such a confirmation has the form of a counterexample to the assumption that it is possible to obtain additional terms of the series involved in the solution that are invariant under all prolongations of the given equation.

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Acknowledgments

The authors are grateful to anonymous referees for their helpful comments, as well as Maplesoft (Waterloo, Canada) for consultations and discussions.

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Authors and Affiliations

  1. Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Vavilova, 40, Moscow, 119333, Russia

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

Authors
  1. S. A. Abramov
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  2. D. E. Khmelnov
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  3. A. A. Ryabenko
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Corresponding author

Correspondence to S. A. Abramov .

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Editors and Affiliations

  1. Université de Lille, Villeneuve d'Ascq, France

    François Boulier

  2. Coventry University, Coventry, UK

    Matthew England

  3. Plekhanov Russian University of Economics, Moscow, Russia

    Timur M. Sadykov

  4. Institute of Theoretical and Applied Mechanics, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Abramov, S.A., Khmelnov, D.E., Ryabenko, A.A. (2022). On Truncated Series Involved in Exponential-Logarithmic Solutions of Truncated LODEs. In: Boulier, F., England, M., Sadykov, T.M., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2022. Lecture Notes in Computer Science, vol 13366. Springer, Cham. https://doi.org/10.1007/978-3-031-14788-3_2

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  • DOI: https://doi.org/10.1007/978-3-031-14788-3_2

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