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Procedures for Searching Laurent and Regular Solutions of Linear Differential Equations with the Coefficients in the Form of Truncated Power Series

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Abstract

Linear ordinary differential equations whose coefficients are infinite (formal) power series given in a truncated form are considered. Computer algebra procedures (implemented in Maple) for constructing solutions of two forms are suggested. The procedures find the greatest number of series terms occurring in the solutions that can be found for the given truncated series—coefficients.

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Notes

  1. The package and the Maple session with examples of use of the procedures described are available at the address http://www. ccas.ru/ca/TruncatedSeries

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Funding

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

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Authors and Affiliations

  1. Dorodnicyn Computing Center, Federal Research Center “Computer Science and Control” of 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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Correspondence to S. A. Abramov, A. A. Ryabenko or D. E. Khmelnov.

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Translated by A. Pesterev

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Abramov, S.A., Ryabenko, A.A. & Khmelnov, D.E. Procedures for Searching Laurent and Regular Solutions of Linear Differential Equations with the Coefficients in the Form of Truncated Power Series. Program Comput Soft 46, 67–75 (2020). https://doi.org/10.1134/S0361768820020024

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  • DOI: https://doi.org/10.1134/S0361768820020024

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