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On Regular and Logarithmic Solutions of Ordinary Linear Differential Systems

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 3718)

Abstract

We present an approach to construct all the regular solutions of systems of linear ordinary differential equations using the desingularization algorithm of Abramov & Bronstein (2001) as an auxiliary tool. A similar approach to find all the solutions with entries in C(z) [log z] is presented as well, together with a new hybrid method for constructing the denominator of rational and logarithmic solutions.

Keywords

  • Regular Solution
  • Initial Segment
  • Laurent Series
  • Polynomial Solution
  • Recurrence System

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Work partially supported by the ECO-NET program of the French Foreign Affairs Ministry, project No. 08119TG, and by RFBR grant No. 04-01-00757.

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© 2005 Springer-Verlag Berlin Heidelberg

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Abramov, S.A., Bronstein, M., Khmelnov, D.E. (2005). On Regular and Logarithmic Solutions of Ordinary Linear Differential Systems. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2005. Lecture Notes in Computer Science, vol 3718. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11555964_1

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  • DOI: https://doi.org/10.1007/11555964_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28966-1

  • Online ISBN: 978-3-540-32070-8

  • eBook Packages: Computer ScienceComputer Science (R0)