An algorithm for computing the formal solutions of differential systems in the neighborhood of an irregular singular point

Authors:
G. Chen
Affiliations:
Equipe de Calcul Parallèle et Calcul Formel, LMC, IMAG-INPG-CNRS, 46, Av. Félix-Viallet, 38031 Grenoble FRANCE
Venue:
ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
Year:
1990

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Abstract

We discuss in this paper an algorithm for the computation of the formal solutions of differential systems in the neighborhood of an irregular singular point. In the reduction of the differential systems, we use its Arnold-Wasow's canonical form. We discuss also an algorithm for the reduction of the differential system to its Arnold-Wasow's canonical form. Then we discuss the results of a shearing transformation on this canonical form and we get the convergence of the algorithm. This paper and [3] consist of a complete study of the problem of computations of the formal solutions of differential systems in the neighborhood of a singular point (regular or irregular).