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

Applicable Algebra in Engineering, Communications and Computing

Volumn 8, Issue 1, 1997, Pages 1-23

  Barkatou, M A ^a  

^a LMC IMAG   (France)

Author keywords

Formal solutions; Linear system of differential equations; Newton polygon; Singular points

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; COMPUTER SYSTEMS; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; POLES AND ZEROS;

FORMAL FUNDAMENTAL MATRIX SOLUTIONS; LINEAR DIFFERENTIAL SYSTEMS; MAPLE COMPUTER ALGEBRA SYSTEM; NEWTON POLYGON; SINGULAR POINTS;

DIFFERENTIAL EQUATIONS;

EID: 0030736135     PISSN: 09381279     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002000050048     Document Type: Article

References (19)

1. Babbitt, D. G., Varadarajan, V. S.: Formal reduction of meromorphic differential equations: a group theoretic view. Pacific J Math 109(1), 1-80 (1983)
2. Chen, G.: An algorithm for computing the formal solutions of differential systems in the neighborhood of an irregular singular point. ISSAC 90, 231-235
3. Balser, W., Jurkat, W. B. Lutz, D. A.: A general thoery of invariants for meromorphic differential equations; Pan I, Formal invariants, Funkcial. Ekvac. 22, 197-227 (1979)
4. Barkatou, M. A.: An algorithm for computing a companion block diagonal form for a system of linear differential equations. AAECC 4, 185-195 (1993)
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)
6. Cope, F.: Formal solutions of irregular linear differential equations. Am. J. Math. 58, 130-140 (1936)
7. Deligne, P.: Equations différentielles à points singuliers réguliers. Lectures Notes in Mathematics, Vol. 163. Berlin, Heidelberg, New York: Springer 1970
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-Fasicule 3, 67-83 (1986)
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
11. Lutz, D. A., Schäfke, R.: On the identification and stability of formal invariants for singular differential equations. Linear Algebra And Its Applications 72, 1-46 (1985)
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)
14. Ramis, J. P.: Théorèmes d'indices Gevrey pour les équations différentielles ordinaires. Pub. IRMA, Strasbourg FRANCE, pp. 57-60 (1981)
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)
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)
19. Wasow, W.: Asymptotic Expansions For Ordinary Differential Equations. Interscience Publishers New-York 1965