Computer Physics Communications Program LibraryPrograms in Physics & Physical Chemistry |

[Licence| Download | New Version Template] adzf_v1_0.tar.gz(16 Kbytes) | ||
---|---|---|

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_0Distribution 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. |

Disclaimer | ScienceDirect | CPC Journal | CPC | QUB |