Algorithms for regular solutions of higher-order linear differential systems

We study systems of higher-order linear differential equations having a regular singularity at the origin. Using the properties of matrix polynomials, we develop efficient methods for computing their regular formal solutions. Our algorithm handles the system directly without transforming it into a system of first-order but higher size. We give its arithmetic complexity and discuss the results of an implementation in Maple. Categories and Subject Descriptors

• Type: Conference
• Year: 2009
• Where: ISSAC
• Authors: Moulay A. Barkatou, Thomas Cluzeau, Carole El Bacha
• Keywords: ISSAC 2009, Linear Differential Equations, Mathematics, Regular Formal Solutions, Regular Singularity