Skip to main content
Log in

An algorithm to compute the exponential part of a formal fundamental matrix solution of a linear differential system

  • Published:
Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

In this paper we describe an efficient algorithm, fully implemented in the Maple computer algebra system, that computes the exponential part of a formal fundamental matrix solution of a linear differential system having a singularity of pole type at the origin.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Babbitt, D. G., Varadarajan, V. S.: Formal reduction of meromorphic differential equations: a group theoretic view. Pacific J Math109(1), 1–80 (1983)

    MATH  MathSciNet  Google Scholar 

  2. Chen, G.: An algorithm for computing the formal solutions of differential systems in the neighborhood of an irregular singular point. ISSAC90, 231–235

  3. Balser, W., Jurkat, W. B., Lutz, D. A.: A general thoery of invariants for meromorphic differential equations; Part I, Formal invariants, Funkcial. Ekvac.22, 197–227 (1979)

    MATH  MathSciNet  Google Scholar 

  4. Barkatou, M. A.: An algorithm for computing a companion block diagonal form for a system of linear differential equations. AAECC4, 185–195 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  5. Barkatou, M. A.: Rational Newton Algorithm for computing formal solutions of linear differential equations, Proc. International Symposium on Algebraic Computation 1988. Berlin, Heidelberg, New York: Springer Lecture Notes in Computer Science vol. 358 (1989)

    Google Scholar 

  6. Cope, F.: Formal solutions of irregular linear differential equations. Am. J. Math.58, 130–140 (1936)

    Article  MathSciNet  Google Scholar 

  7. Deligne, P.: Equations différentielles à points singuliers réguliers. Lectures Notes in Mathematics, Vol.163. Berlin, Heidelberg, New York: Springer 1970

    Google Scholar 

  8. Hilali, A.: Solutions formelles de systèmes différentiels linéaires au voisinage d’un point singulier. Thèse de l’université Joseph Fourier Grenoble France, Juin 1987, pp. 71–103

  9. Hilali, A., Wazner, A.: Un algorithme de calcul de l’invariant de Katz d’un système différentiel linéaire. Annales de l’Institut Fourier, Tome XXXVI-Fasicule3, 67–83 (1986)

    MathSciNet  Google Scholar 

  10. Levelt, A. H. M.: Stabilizing differential operators: a method for computing invariants at irregular singularities. In: Singer, M. (ed), Differential Equations and Computer Algebra, Computational Mathematics and Applications, 181–228. New York: Academic Press 1991

    Google Scholar 

  11. Lutz, D. A., Schäfke, R.: On the identification and stability of formal invariants for singular differential equations. Linear Algebra And Its Applications72, 1–46 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  12. Malgrange, B.: Sur le réduction formelle des équations différentielles à singularités irrégulières, Preprint Grenoble 1979

  13. Moser, J.: The order of a singularity in Fuchs’ theory, Math. Z.72, 379–398 (1960)

    Article  MATH  MathSciNet  Google Scholar 

  14. Ramis, J. P.: Théorèmes d’indices Gevrey pour les équations différentielles ordinaires. Pub. IRMA, Strasbourg FRANCE, pp. 57–60 (1981)

    Google Scholar 

  15. Sommeling, R.: Characteristic classes for irregular singularies. PhD thesis, University of Nijmegen, 1993

  16. Tournier, E.: Solutions formelles d’équations différentielles. Thèse de l’université Joseph Fourier Grenoble France, Avril 1987

  17. Robba, P.: Lemmes de Hensel pour les opérateurs différentiels. Application à la réduction formelle des équations différentielles. L’Enseigenment Mathématique, Ser. II,26, 279–311 (1980)

    MATH  MathSciNet  Google Scholar 

  18. Turritin, H. L.: Convergent solutions of ordinary linear homogeneous differential equations in the neighborhood of an irregular singular point. Acta Matm.93, 27–66 (1955)

    Article  Google Scholar 

  19. Wasow, W.: Asymptotic Expansions For Ordinary Differential Equations. Interscience Publishers New-York 1965

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. A. Barkatou.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Barkatou, M.A. An algorithm to compute the exponential part of a formal fundamental matrix solution of a linear differential system. AAECC 8, 1–23 (1997). https://doi.org/10.1007/s002000050048

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s002000050048

Keywords

Navigation