Programs 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_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).|
Nature of problem:
Solution of rational first order ordinary differential equations.
The method of solution is based on a Darboux/PS type approach.
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.
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 , it can successfully solve a class of rational first order ODEs that were not solved by some of the best-known ODE solvers available.
This depends strongly on the ODE, but usually under 4 seconds.
|||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.|
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