On the reduction of singularly-perturbed linear differential systems

In this article, we treat the turning points of singularly-perturbed linear differential systems and reduce their parameter singularity's rank to its minimal integer value. Our approach is Moser-based, i.e. it is based on the reduction criterion introduced for singular linear differential systems by Moser [21]. Such algorithms have proved their utility in the symbolic resolution of the systems of linear functional equations [5, 6, 8], giving rise to the package ISOLDE [7], as well as in the perturbed algebraic eigenvalue problem [13]. In particular, we generalize the Moser-based algorithm described in [4]. Our algorithm, implemented in the computer algebra system Maple, paves the way for efficient symbolic resolution of singularly-perturbed linear differential systems as well as further applications of Moser-based reduction over bivariate (differential) fields [1].