Simple forms of higher-order linear differential systems and their applications in computing regular solutions

DOI10.1016/j.jsc.2011.01.001zbMath1216.34096OpenAlexW2025071884MaRDI QIDQ2430021

Moulay A. Barkatou, Carole El Bacha, Thomas Cluzeau

Publication date: 5 April 2011

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

Full work available at URL: https://doi.org/10.1016/j.jsc.2011.01.001

zbMATH Keywords

singularitiescomputer algebramatrix polynomialsregular formal solutionshigher-order linear differential systems

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Formal solutions and transform techniques for ordinary differential equations in the complex domain (34M25) Linear ordinary differential equations and systems in the complex domain (34M03)

Related Items (8)

On rational solutions of pseudo-linear systems ⋮ Procedures for searching local solutions of linear differential systems with infinite power series in the role of coefficients ⋮ On \(k\)-simple forms of first-order linear differential systems and their computation ⋮ On singular points of solutions of linear differential systems with polynomial coefficients ⋮ Formal reduction of singular linear differential systems using eigenrings: a refined approach ⋮ Linear differential and difference systems: \(\mathrm{EG}_\delta\)- and \(\mathrm{EG}_\sigma\)-eliminations ⋮ Regular solutions of linear differential systems with power series coefficients ⋮ On the Differential and Full Algebraic Complexities of Operator Matrices Transformations

Uses Software

• Isolde

Cites Work

• Formal reduction theory of meromorphic differential equations: a group theoretic view
• Remarks on the formulation of the Cauchy problem for general system of ordinary differential equations
• Formal power series and linear systems of meromorphic ordinary differential equations
• Fraction-free row reduction of matrices of Ore polynomials.
• The order of a singularity in Fuchs' theory
• Fraction-Free Computation of Matrix Rational Interpolants and Matrix GCDs
• Algorithms for regular solutions of higher-order linear differential systems
• Efficient computation of order bases
• On solutions of linear functional systems
• EG-eliminations
• Asymptotically fast polynomial matrix algorithms for multivariable systems
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