Generalized ODE reduction algorithm with bounded degree transformation

2025/08/13 by Huang, Shaoxuan
#FOS: Computer and information sciences #Symbolic Computation (cs.SC)

paper · doi:10.48550/arxiv.2508.09754

Abstract

As a generalization of our previous result\citehuang2025algorithm, this paper aims to answer the following question: Given a 2-dimensional polynomial vector field y^′=(M(x,y))/(N(x,y)), how to find a rational transformation y → (A(x,y))/(B(x,y)) with bounded degree numerator, the inverse of which transforms this vector field into a simpler form y^′=∑_i=0ⁿf_i(x)yⁱ. Such a structure, often known as the generalized Abel equation and has been studied in various areas, provides a deeper insight into the property of the original vector field. We have implemented an algorithm with considerable performance to tackle this problem and the code is available in \hrefhttps://www.researchgate.net/publication/393362858_Generalized_ODE_reduction_algorithmResearchgate.

Citations

• Symbolic Computations of First Integrals for Polynomial Vector Fields
• First order ODEs, Symmetries and Linear Transformations

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