Lsolver

Determining Liouvillian first integrals for dynamical systems in the plane. Here we present/implement a semi-algorithm to find Liouvillian first integrals of dynamical systems in the plane. The algorithm is based on a Darboux-type procedure to find the integrating factor for the system. Since the particular form of such systems allows reducing it to a single rational first order ordinary differential equation (rational first order ODE), the Lsolver package presents a set of software routines in Maple for dealing with rational first order ODEs. The package present commands permitting research investigations of some algebraic properties of the system that is being studied.

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References in zbMATH (referenced in 4 articles )

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  1. Chèze, Guillaume; Combot, Thierry: Symbolic computations of first integrals for polynomial vector fields (2020)
  2. Avellar, J.; Cardoso, M. S.; Duarte, L. G. S.; da Mota, L. A. C. P.: Determining Liouvillian first integrals for dynamical systems in the plane and an integrability analysis (2014)
  3. Avellar, J.; Duarte, L. G. S.; Duarte, S. E. S.; Da Mota, L. A. C. P.: Determining Liouvillian first integrals for dynamical systems in the plane (2007)
  4. Avellar, J.; Duarte, L. G. S.; Duarte, S. E. S.; da Mota, L. A. C. P.: Integrating first-order differential equations with Liouvillian solutions via quadratures: a semi-algorithmic method (2005)