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The TruncatedSeries Package for Solving Linear Ordinary Differential Equations Having Truncated Series Coefficients

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Maple in Mathematics Education and Research (MC 2020)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1414))

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Abstract

We consider linear ordinary differential equations with power series in the role of coefficients. It is assumed that some or all of the series are truncated. A series of the form \(\varSigma \, a_ix^i\) can also be given completely using an algorithm that computes \(a_i\) from i. The equation may contain both types of coefficients—truncated and represented algorithmically. Algorithms and commands that implement them in Maple as the TruncatedSeries package are proposed, which make it possible to find Laurent, regular and exponential-logarithmic solutions. In cases where, due to the presence of truncated coefficients, the information about the equation is incomplete, commands of our package find the maximum possible number of terms of those series that are involved in the solutions. If all the coefficients of the given equation are algorithmically represented series then the commands allow finding any specified number of initial terms of the series involved in the solutions.

Supported by RFBR grant, project 19-01-00032.

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Authors and Affiliations

  1. Dorodnicyn Computing Centre, 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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Editors and Affiliations

  1. Western University, London, ON, Canada

    Robert M. Corless

  2. Maplesoft, Waterloo, ON, Canada

    Jürgen Gerhard

  3. Wilfrid Laurier University, Waterloo, ON, Canada

    Ilias S. Kotsireas

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Abramov, S.A., Khmelnov, D.E., Ryabenko, A.A. (2021). The TruncatedSeries Package for Solving Linear Ordinary Differential Equations Having Truncated Series Coefficients. In: Corless, R.M., Gerhard, J., Kotsireas, I.S. (eds) Maple in Mathematics Education and Research. MC 2020. Communications in Computer and Information Science, vol 1414. Springer, Cham. https://doi.org/10.1007/978-3-030-81698-8_2

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  • DOI: https://doi.org/10.1007/978-3-030-81698-8_2

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  • Publisher Name: Springer, Cham

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