An algorithm computing the regular formal solutions to a system of linear differential equations

DOI10.1006/jsco.1999.0315zbMath0951.34066OpenAlexW2052387938MaRDI QIDQ1974704

Eckhard Pflügel, Moulay A. Barkatou

Publication date: 8 May 2000

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jsco.1999.0315

zbMATH Keywords

linear differential equationsformal matrix power seriesregular formal solutions

Mathematics Subject Classification ID

Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Linear ordinary differential equations and systems (34A30) Formal solutions and transform techniques for ordinary differential equations in the complex domain (34M25)

Related Items (13)

On rational solutions of pseudo-linear systems ⋮ Formal solutions of singularly-perturbed linear differential systems ⋮ Formal reduction of singular linear differential systems using eigenrings: a refined approach ⋮ Regular solutions of linear ordinary differential equations and truncated series ⋮ On matrix perturbations with minimal leading Jordan structure. ⋮ Procedures for searching Laurent and regular solutions of linear differential equations with the coefficients in the form of truncated power series ⋮ On rational solutions of systems of linear differential equations ⋮ Fuchsia: a tool for reducing differential equations for Feynman master integrals to epsilon form ⋮ Formal solutions of completely integrable Pfaffian systems with normal crossings ⋮ ON MULTISERVER RETRIAL QUEUES: HISTORY, OKUBO-TYPE HYPERGEOMETRIC SYSTEMS AND MATRIX CONTINUED-FRACTIONS ⋮ A monomial-by-monomial method for computing regular solutions of systems of pseudo-linear equations ⋮ Linear differential and difference systems: \(\mathrm{EG}_\delta\)- and \(\mathrm{EG}_\sigma\)-eliminations ⋮ Regular solutions of linear differential systems with power series coefficients

Uses Software

• Maple
• DESIR

Cites Work

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• Formes super-irréductibles des systèmes différentiels linéaires. (Super-irreducible forms of linear differential systems)
• Liouvillian solutions of linear differential equations with Liouvillian coefficients
• An algorithm for computing a companion block diagonal form for a system of linear differential equations
• An algorithm to compute the exponential part of a formal fundamental matrix solution of a linear differential system
• On the latest version of DESIR-II
• On rational solutions of systems of linear differential equations
• The order of a singularity in Fuchs' theory
• Convergent solutions of ordinary linear homogeneous differential equations in the neighborhood of an irregular singular point
• Über regulär-singuläre Lösungen von Systemen linearer Differentialgleichungen. I.

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