On the Reduction of Singularly-Perturbed Linear Differential Systems

TL;DR

This paper presents a Moser-based algorithm for reducing the rank of singularities in linear differential systems, facilitating their symbolic resolution and applications in algebraic eigenvalue problems.

Contribution

It introduces a novel Moser-based reduction algorithm for singularly-perturbed linear differential systems, implemented in Maple, enhancing symbolic resolution capabilities.

Findings

Effective reduction of singularity rank in differential systems

Implementation in Maple improves computational efficiency

Facilitates symbolic solutions and further applications

Abstract

In this article, we recover singularly-perturbed linear differential systems from their turning points and reduce the rank of the singularity in the parameter to its minimal integer value. Our treatment is Moser-based; that is to say it is based on the reduction criterion introduced for linear singular differential systems by Moser. Such algorithms have proved their utility in the symbolic resolution of the systems of linear functional equations, giving rise to the package ISOLDE, as well as in the perturbed algebraic eigenvalue problem. 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.