A Linear Prelle-Singer method
L.G.S. Duarte, H.S. Ferreira, L.A.C.P. da Mota
TL;DR
This paper introduces a linear method to identify Darboux polynomials in polynomial vector fields, extending the Prelle-Singer approach to rational second-order ODEs with elementary integrals.
Contribution
The paper presents a novel linear procedure for finding Darboux polynomials, enhancing the Prelle-Singer method for polynomial and rational 2ODEs.
Findings
Linear procedure effectively finds Darboux polynomials
Extension to rational 2ODEs with elementary integrals
Improves efficiency of integrability analysis
Abstract
The Prelle-Singer method allows determining an elementary first integral admitted by a polynomial vector field in the plane. It is a semi-algorithm whose nonlinear step consists of determining the Darboux polynomials of the vector field. In this article we construct a linear procedure to determine the Darboux polynomials present in the integrating factor of a polynomial vector field in the plane. Next, we extend the procedure to deal with rational 2ODEs that admit an elementary first integral
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Taxonomy
TopicsMatrix Theory and Algorithms