On the Moser- and super-reduction algorithms of systems of linear differential equations and their complexity

DOI10.1016/j.jsc.2009.01.002zbMath1183.34134OpenAlexW2067639492MaRDI QIDQ1023266

Eckhard Pflügel, Moulay A. Barkatou

Publication date: 11 June 2009

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

Full work available at URL: https://doi.org/10.1016/j.jsc.2009.01.002

zbMATH Keywords

singularitiescomputer algebrasuper-reductionMoser-reductionlocal analysis of linear differential systems

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Numerical methods for ordinary differential equations (65L99) Software, source code, etc. for problems pertaining to ordinary differential equations (34-04)

Related Items (8)

On rational solutions of pseudo-linear systems ⋮ Reducing differential equations for multiloop master integrals ⋮ On \(k\)-simple forms of first-order linear differential systems and their computation ⋮ Formal solutions of singularly-perturbed linear differential systems ⋮ Formal reduction of singular linear differential systems using eigenrings: a refined approach ⋮ Unnamed Item ⋮ On ramification indices of formal solutions of constructive linear ordinary differential systems ⋮ A monomial-by-monomial method for computing regular solutions of systems of pseudo-linear equations

Uses Software

• Isolde

Cites Work

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• Formes super-irréductibles des systèmes différentiels linéaires. (Super-irreducible forms of linear differential systems)
• The solution of the matrix equations \(AXB-CXD=E\) and \((YA-DZ,YC- BZ)=(E,F)\)
• Zur Reduktion von linearen Differentialgleichungssystemen
• 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
• Computing rational forms of integer matrices
• An improved estimate for the maximal growth order of solutions of linear differential systems
• Effective formal reduction of linear differential systems
• On rational solutions of systems of linear differential equations
• The order of a singularity in Fuchs' theory

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