On \(k\)-simple forms of first-order linear differential systems and their computation

DOI10.1016/j.jsc.2013.01.003zbMath1277.34011OpenAlexW2025664247MaRDI QIDQ386984

Moulay A. Barkatou, Carole El Bacha

Publication date: 11 December 2013

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

Full work available at URL: https://doi.org/10.1016/j.jsc.2013.01.003

zbMATH Keywords

Newton polygonlocal invariantsMapleformal solutions\(k\)-simple formsFirst-order linear differential systemsminimal Poincaré-rankregular/irregular singularitiessuper-reduction

Mathematics Subject Classification ID

Explicit solutions, first integrals of ordinary differential equations (34A05) Linear ordinary differential equations and systems (34A30) Numerical methods for ordinary differential equations (65L99) Software, source code, etc. for problems pertaining to ordinary differential equations (34-04)

Related Items (4)

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 ⋮ Formal solutions of completely integrable Pfaffian systems with normal crossings

Uses Software

• Maple

Cites Work

• Formal reduction theory of meromorphic differential equations: a group theoretic view
• On the Moser- and super-reduction algorithms of systems of linear differential equations and their complexity
• Formes super-irréductibles des systèmes différentiels linéaires. (Super-irreducible forms of linear differential systems)
• An algorithm to compute the exponential part of a formal fundamental matrix solution of a linear differential system
• On super-irreducible forms of linear differential systems with rational function coefficients.
• Effective formal reduction of linear differential systems
• On rational solutions of systems of linear differential equations
• Simple forms of higher-order linear differential systems and their applications in computing regular solutions
• The order of a singularity in Fuchs' theory
• Simultaneously row- and column-reduced higher-order linear differential systems
• Computing closed form solutions of integrable connections
• Solving linear ordinary differential systems in hyperexponential extensions
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