Rational solutions of first-order algebraic ordinary difference equations

Thieu N. Vo; Yi Zhang

doi:10.1016/j.aam.2020.102018

Rational solutions of first-order algebraic ordinary difference equations

Thieu N. Vo
, Yi Zhang^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We propose an algebraic geometric approach for studying rational solutions of first-order algebraic ordinary difference equations (AOΔEs). For an autonomous first-order AOΔE, we give an upper bound for the degrees of its rational solutions, and thus derive a complete algorithm for computing corresponding rational solutions.

Original language	English
Article number	102018
Journal	Advances in Applied Mathematics
Volume	117
DOIs	https://doi.org/10.1016/j.aam.2020.102018
Publication status	Published - Jun 2020
Externally published	Yes

Keywords

Algebraic ordinary difference equations
Algorithms
Parametrization
Resultant theory
Separable difference equation
Strong rational general solutions

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10.1016/j.aam.2020.102018

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title = "Rational solutions of first-order algebraic ordinary difference equations",

abstract = "We propose an algebraic geometric approach for studying rational solutions of first-order algebraic ordinary difference equations (AOΔEs). For an autonomous first-order AOΔE, we give an upper bound for the degrees of its rational solutions, and thus derive a complete algorithm for computing corresponding rational solutions.",

keywords = "Algebraic ordinary difference equations, Algorithms, Parametrization, Resultant theory, Separable difference equation, Strong rational general solutions",

author = "Vo, \{Thieu N.\} and Yi Zhang",

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

year = "2020",

month = jun,

doi = "10.1016/j.aam.2020.102018",

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volume = "117",

journal = "Advances in Applied Mathematics",

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T1 - Rational solutions of first-order algebraic ordinary difference equations

AU - Vo, Thieu N.

AU - Zhang, Yi

PY - 2020/6

Y1 - 2020/6

N2 - We propose an algebraic geometric approach for studying rational solutions of first-order algebraic ordinary difference equations (AOΔEs). For an autonomous first-order AOΔE, we give an upper bound for the degrees of its rational solutions, and thus derive a complete algorithm for computing corresponding rational solutions.

AB - We propose an algebraic geometric approach for studying rational solutions of first-order algebraic ordinary difference equations (AOΔEs). For an autonomous first-order AOΔE, we give an upper bound for the degrees of its rational solutions, and thus derive a complete algorithm for computing corresponding rational solutions.

KW - Algebraic ordinary difference equations

KW - Algorithms

KW - Parametrization

KW - Resultant theory

KW - Separable difference equation

KW - Strong rational general solutions

UR - https://www.scopus.com/pages/publications/85079347695

U2 - 10.1016/j.aam.2020.102018

DO - 10.1016/j.aam.2020.102018

M3 - Article

AN - SCOPUS:85079347695

SN - 0196-8858

VL - 117

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

M1 - 102018

ER -

Rational solutions of first-order algebraic ordinary difference equations

Abstract

Keywords

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