Computer Physics Communications Program Library

Programs in Physics & Physical Chemistry



Manuscript Title: Determining Liouvillian First Integrals for Dynamical Systems in the Plane
Authors: J. Avellar, L.G.S. Duarte, S.E.S. Duarte, L.A.C.P. da Mota
Program title: Lsolver
Catalogue identifier: ADZF_v1_0 Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 177(2007)584
Programming language: Maple.
Computer: Any computer running Maple.
Operating system: Windows ME, Windows XP.
Keywords: Liouvillian functions, first integrals, dynamical systems in the plane, first order ordinary differential equations, computer algebra, Prelle-Singer (PS).
PACS: 02.30.Hq.
Classification: 4.3.
Nature of problem: Solution of rational first order ordinary differential equations.
Solution method: The method of solution is based on a Darboux/PS type approach.
Restrictions: If the integrating factor for the ODE under consideration presents Darboux Polynomials of high degree ( > 3 ) in the dependent and independent variables, the package may spend an impractical amount of time to obtain the solution.
Unusual features: Our implementation not only searches for Liouvillian conserved quantities, but can also be used as a research tool that allows the user to follow all the steps of the procedure (for example, we can calculate the algebraic invariants curves and associated co-factors, the integrating factor etc). In addition, since our package is based on recent theoretical developments [1], it can successfully solve a class of rational first order ODEs that were not solved by some of the best-known ODE solvers available.
Running time: This depends strongly on the ODE, but usually under 4 seconds.
References:
[1]	J. Avellar, L.G.S. Duarte, S.E.S. Duarte, L.A.C.P. da Mota, Integrating First-Order Differential Equations with Liouvillian Solutions via Quadratures: a Semi-Algorithmic Method, Journal of Computational and Applied Mathematics 182 (2005) 327-332.