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European Computer Algebra Conference

EUROCAM 1982: Computer Algebra pp 273–280Cite as

An algorithm to obtain formal solutions of a linear homogeneous differential equation at an irregular singular point

  • 8. Applications II
  • Conference paper
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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 144))

Abstract

The algorithm DELIRE (Linear Differential Equation Irregular and REgular singularities) presented in this paper gives the formal solutions (normal and sub-normal) at an irregular singular point of a linear homogeneous differential operator, whose coefficients are formal Puiseux series [11].

This algorithm (greatly inspired by recent works of B. Malgrange) is based on the use of the Newton polygon of the differential operator studied.

The part of DELIRE which gives the solutions in the neighborhood of singular regular points has been presented in [3].

DELIRE is included in the general algorithm said DESIR (Differential Equation System Irregular and Regular singularities), which deals with linear homogeneous differential system in the complex plan.

work supported by the CNRS under ATP no 023.

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References

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Author information

Authors and Affiliations

  1. Laboratoire IMAG, B.P. 53 X, 38041, Grenoble cédex, France

    J. Della Dora, Cl. Di Crescenzo & E. Tournier

Authors
  1. J. Della Dora
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  2. Cl. Di Crescenzo
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  3. E. Tournier
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Editor information

Jacques Calmet

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© 1982 Springer-Verlag Berlin Heidelberg

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Della Dora, J., Di Crescenzo, C., Tournier, E. (1982). An algorithm to obtain formal solutions of a linear homogeneous differential equation at an irregular singular point. In: Calmet, J. (eds) Computer Algebra. EUROCAM 1982. Lecture Notes in Computer Science, vol 144. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-11607-9_32

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  • DOI: https://doi.org/10.1007/3-540-11607-9_32

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11607-3

  • Online ISBN: 978-3-540-39433-4

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