Skip to main content
SpringerLink
Log in

Rational Newton algorithm for computing formal solutions of linear differential equations

  • Differential Equations
  • Conference paper
  • First Online:
Symbolic and Algebraic Computation (ISSAC 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 358))

Included in the following conference series:

Abstract

In this paper we present a new algorithm for solving linear differential equations in the neighbourhood of an irregular singular point. This algorithm is based upon the same principles as Newton algorithm, however it has a lower cost and is more suitable for computing algebra.

Work supported by the PRC Mathématiques et informatique du CNRS and by the Greco Calcul Formel du CNRS.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. Della Dora et E. Tournier: Solutions formelles d'équations différentielles au voisinage depoints singuliers réguliers. RR no 239 février 1981-IMAG.

    Google Scholar 

  2. J. Della Dora et E. Tournier: An algorithm to obtain formal solutions of a linear homogeneous differential equation at an irregular singular point. in. Computer Algebra.

    Google Scholar 

  3. D.Duval: Diverses questions relatives au calcul formel avec nombres algébriques. Thése d'Etat-Faculté des Sciences de Grenoble-1987

    Google Scholar 

  4. E. L. Ince: Ordinary differential equations, Dover-New York-1944.

    Google Scholar 

  5. B. Malgrange: Sur la réduction formelle des équations différentielles à singularités irrégulières. preprint Institut Fourier-1981

    Google Scholar 

  6. E. Tournier: Solutions formelles d'équations differentielles. Thèse d'Etat-Faculté des Sciences de Grenoble-1987

    Google Scholar 

  7. A. Barkatou: Alogorithme de Newton rationnel pour le calcul des solutions formelles d'une équation différentielle linéaire en un point singulier irrégulier. RR no 704 février 1988-IMAG.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Equipe de Calcul Formel et parallélisme laboratoire TIM3 CNRS, INPG, IMAG, 46, avenue Félix Viallet, 38031, Grenoble Cedex

    M. A. Barkatou

Authors
  1. M. A. Barkatou
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

P. Gianni

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Barkatou, M.A. (1989). Rational Newton algorithm for computing formal solutions of linear differential equations. In: Gianni, P. (eds) Symbolic and Algebraic Computation. ISSAC 1988. Lecture Notes in Computer Science, vol 358. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51084-2_17

Download citation

  • DOI: https://doi.org/10.1007/3-540-51084-2_17

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51084-0

  • Online ISBN: 978-3-540-46153-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation