Carole El Bacha - University of Limoges ; CNRS ; XLIM UMR6172 ; DMI

Simultaneously Row- and Column-Reduced Higher-Order Linear Differential Systems.

Abstract: In this talk, we investigate the local analysis of systems of linear differential-algebraic equations (DAEs) and second order linear differential systems. 
We show how one can transform an input linear DAE into a reduced form that allows for the decoupling of the differential and algebraic
components of the system. Classification of singularities of DAEs are defined and discussed. Then, we extend this approach to second order linear differential 
systems and discuss various applications: classification of singularities and computation of regular solutions. This talk is the first step towards a generalisation 
of the formal reduction of first-order ODEs to higher-order systems. 
Our algorithm for first order DAEs has been implemented in the computer algebra system Maple as part of the ISOLDE package. 

This is a joint work with M. Barkatou and E. Pfluegel.