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Linear differential, difference and q-difference homogeneous equations having no rational solutions

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A. GheffarAuthors Info & Claims

ACM Communications in Computer Algebra, Volume 44, Issue 3/4

Pages 78 - 83

https://doi.org/10.1145/1940475.1940525

Published: 28 January 2011 Publication History

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Abstract

Some changes of the traditional scheme for finding rational solutions of linear differential, difference and q-difference homogeneous equations with rational coefficients are proposed. In many cases these changes allow one to predict the absence of rational solutions in an early stage of the computation.

References

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Abramov SKhmelnov DRyabenko A(2020)Checkpoints in searching for rational solutions of linear ordinary difference and differential systemsACM Communications in Computer Algebra10.1145/3427218.342721954:2(18-29)Online publication date: 29-Sep-2020
https://dl.acm.org/doi/10.1145/3427218.3427219
Abramov SRyabenko AKhmelnov D(2018)Laurent, Rational, and Hypergeometric Solutions of Linear q-Difference Systems of Arbitrary Order with Polynomial CoefficientsProgramming and Computing Software10.1134/S036176881802002044:2(120-130)Online publication date: 1-Mar-2018
https://dl.acm.org/doi/10.1134/S0361768818020020
Gheffar A(2015)Detecting Nonexistence of Rational Solutions of Linear Difference Equations in Early Stages of ComputationACM Communications in Computer Algebra10.1145/2733693.273369748:3/4(90-97)Online publication date: 5-Feb-2015
https://dl.acm.org/doi/10.1145/2733693.2733697

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Linear differential, difference and q-difference homogeneous equations having no rational solutions

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cover image ACM Communications in Computer Algebra

ACM Communications in Computer Algebra Volume 44, Issue 3/4

September/December 2010

145 pages

ISSN:1932-2232

EISSN:1932-2240

DOI:10.1145/1940475

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Association for Computing Machinery

New York, NY, United States

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Published: 28 January 2011

Published in SIGSAM-CCA Volume 44, Issue 3/4

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Abramov SKhmelnov DRyabenko A(2020)Checkpoints in searching for rational solutions of linear ordinary difference and differential systemsACM Communications in Computer Algebra10.1145/3427218.342721954:2(18-29)Online publication date: 29-Sep-2020
https://dl.acm.org/doi/10.1145/3427218.3427219
Abramov SRyabenko AKhmelnov D(2018)Laurent, Rational, and Hypergeometric Solutions of Linear q-Difference Systems of Arbitrary Order with Polynomial CoefficientsProgramming and Computing Software10.1134/S036176881802002044:2(120-130)Online publication date: 1-Mar-2018
https://dl.acm.org/doi/10.1134/S0361768818020020
Gheffar A(2015)Detecting Nonexistence of Rational Solutions of Linear Difference Equations in Early Stages of ComputationACM Communications in Computer Algebra10.1145/2733693.273369748:3/4(90-97)Online publication date: 5-Feb-2015
https://dl.acm.org/doi/10.1145/2733693.2733697

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Linear partial q-difference equations on q-linear lattices and their bivariate q-orthogonal polynomial solutions

Polynomial solutions of differential-difference equations

Mode-Dependent Finite-Difference Discretization of Linear Homogeneous Differential Equations

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Linear partial q-difference equations on q-linear lattices and their bivariate q-orthogonal polynomial solutions

Polynomial solutions of differential-difference equations

Mode-Dependent Finite-Difference Discretization of Linear Homogeneous Differential Equations

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