Integrating first-order differential equations with Liouvillian solutions via quadratures: a semi-algorithmic method

DOI10.1016/j.cam.2004.12.014zbMath1071.65095OpenAlexW2083680135MaRDI QIDQ557767

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

Publication date: 30 June 2005

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2004.12.014

zbMATH Keywords

numerical exampleFirst-order ordinary differential equationsIntegrability by quadraturesIntegrating factorLiouvillian functionssemi-algorithmic method

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (6)

A Maple package to find first order differential invariants of 2ODEs via a Darboux approach ⋮ Dealing with rational second order ordinary differential equations where both Darboux and Lie find it difficult: the \(S\)-function method ⋮ Symbolic computations of first integrals for polynomial vector fields ⋮ An efficient method for computing Liouvillian first integrals of planar polynomial vector fields ⋮ Determining Liouvillian first integrals for dynamical systems in the plane ⋮ Finding elementary first integrals for rational second order ordinary differential equations

Uses Software

• Lsolver

Cites Work

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• Lifting canonical algorithms from a ring R to the ring R[x]
• Computing closed form solutions of first order ODEs using the Prelle- Singer procedure
• Elementary First Integrals of Differential Equations
• Liouvillian 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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