Search of rational solutions to differential and difference systems by means of formal series

DOI10.1134/S0361768815020024zbMath1344.34023MaRDI QIDQ2629394

Sergey A. Abramov

Publication date: 6 July 2016

Published in: Programming and Computer Software (Search for Journal in Brave)

zbMATH Keywords

polynomial coefficientsrational solutionsformal series

Mathematics Subject Classification ID

Theoretical approximation of solutions to ordinary differential equations (34A45) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Explicit solutions, first integrals of ordinary differential equations (34A05) Linear ordinary differential equations and systems (34A30) Linear difference equations (39A06)

Related Items (8)

Reducing triangular systems of ODEs with rational coefficients, with applications to coupled Regge-Wheeler equations ⋮ A package of procedures and functions for construction and inversion of analytic mappings with unit Jacobian ⋮ Solving the Cauchy problem for a three-dimensional difference equation in a parallelepiped ⋮ Evaluating the rational generating function for the solution of the Cauchy problem for a two-dimensional difference equation with constant coefficients ⋮ Computational problems of multivariate hypergeometric theory ⋮ Particular solutions of linear differential and (\(q\)-) difference systems with hypergeometric right-hand sides ⋮ Solving the Cauchy problem for a two-dimensional difference equation at a point using computer algebra methods ⋮ When the Search for Solutions Can Be Terminated

Uses Software

• RatDiff

Cites Work

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• Valuations of rational solutions of linear difference equations at irreducible polynomials
• Search for polynomial solutions of linear functional systems by means of induced recurrences
• Rational solutions of linear difference equations: universal denominators and denominator bounds
• Denominators of rational solutions of linear difference systems of an arbitrary order
• On singular points of solutions of linear differential systems with polynomial coefficients
• Factorization of Polynomials and GCD Computations for Finding Universal Denominators
• EG-eliminations
• On the Dimension of Solution Spaces of Full Rank Linear Differential Systems
• Linear differential, difference and q -difference homogeneous equations having no rational solutions
• Detecting Nonexistence of Rational Solutions of Linear Difference Equations in Early Stages of Computation

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