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Procedures for Constructing Truncated Solutions of Linear Differential Equations with Infinite and Truncated Power Series in the Role of Coefficients

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Abstract

In this paper, we propose a package for symbolic construction of exponential–logarithmic solutions to linear differential equations whose coefficients are represented in incomplete form, i.e., as power series for which only a finite number of initial terms is known. The series involved in the solutions are also represented in incomplete form. For each such series, the maximum possible number of initial terms is constructed, which are uniquely determined by known terms of coefficients of a given equation. Additionally, the truncation degree of each series in a solution should not exceed a value specified by the user. It ensures the termination of the computation even when any number of the terms of the series involved in the solution can be defined by known terms of the coefficients of a given equation.

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Notes

  1. The package and Maple sessions with usage examples are available at http://www.ccas.ru/ca/TruncatedSeries.

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ACKNOWLEDGMENTS

We are grateful to Maplesoft (Waterloo, Canada) for consultations and discussions.

Funding

This work was supported in part by the Russian Foundation for Basic Research, grant no. 19-01-00032.

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Authors and Affiliations

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

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

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

Correspondence to S. A. Abramov, A. A. Ryabenko or D. E. Khmelnov.

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Translated by Yu. Kornienko

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Abramov, S.A., Ryabenko, A.A. & Khmelnov, D.E. Procedures for Constructing Truncated Solutions of Linear Differential Equations with Infinite and Truncated Power Series in the Role of Coefficients. Program Comput Soft 47, 144–152 (2021). https://doi.org/10.1134/S036176882102002X

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  • DOI: https://doi.org/10.1134/S036176882102002X

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