Determining Liouvillian first integrals for dynamical systems in the plane

DOI10.1016/j.cpc.2007.05.014zbMath1196.34001arXivmath-ph/0605035OpenAlexW1986000370MaRDI QIDQ710161

L. G. S. Duarte, S. E. S. Duarte, J. Avellar, L. A. C. P. da Mota

Publication date: 18 October 2010

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0605035

zbMATH Keywords

computer algebrafirst integralsfirst order ordinary differential equationsLiouvillian functions\texttt{Lsolver}dynamical systems in the planePrelle-Singer (PS)

Mathematics Subject Classification ID

Explicit solutions, first integrals of ordinary differential equations (34A05) Software, source code, etc. for problems pertaining to ordinary differential equations (34-04)

Related Items (4)

A Maple package to find first order differential invariants of 2ODEs via a Darboux approach ⋮ A generalization of the \(S\)-function method applied to a Duffing-van der Pol forced oscillator ⋮ Dealing with rational second order ordinary differential equations where both Darboux and Lie find it difficult: the \(S\)-function method ⋮ An efficient method for computing Liouvillian first integrals of planar polynomial vector fields

Uses Software

• Maple
• ODEtools
• Lsolver

Cites Work

• Integrating first-order differential equations with Liouvillian solutions via quadratures: a semi-algorithmic method
• Lifting canonical algorithms from a ring R to the ring R[x]
• Computer algebra solving of first order ODEs using symmetry methods
• Computer algebra solving second order ODEs using symmetry methods
• Computing closed form solutions of first order ODEs using the Prelle- Singer procedure
• An extension of the Prelle-Singer method and a Maple implementation
• Elementary First Integrals of Differential Equations
• A method to tackle first-order ordinary differential equations with Liouvillian functions in the solution
• Analysing the structure of the integrating factors for first-order ordinary differential equations with Liouvillian functions in the solution
• Solving second-order ordinary differential equations by extending the Prelle-Singer method
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