Rational Solutions of First-Order Algebraic Ordinary Difference Equations

2019/01/30 by Thieu N. Vo, Yi Zhang, Vo, Thieu N. +1
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Computer and information sciences #FOS: Mathematics #Polynomial and algebraic computation #Symbolic Computation (cs.SC) #cs.SC #math.AC #math.AG

paper · pdf · doi:10.48550/arxiv.1901.11048

openalex publication_date 2019/01/30 · arxiv created 2019/02/01 · arxiv updated 2019/02/05 · openalex created_date 2019/02/21 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Rational Solutions of High-Order Algebraic Ordinary Differential Equations

Related

• Solutions to the First Order Difference Equations in the Multivariate Difference Field
• Rational Solutions of High-Order Algebraic Ordinary Differential Equations
• Rational Solutions to the First Order Difference Equations in the Bivariate Difference Field
• Algorithmic Reduction and Rational General Solutions of First Order Algebraic Differential Equations
• Rational Solutions of Parametric First-Order Algebraic Differential Equations