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[Licence| Download | New Version Template] aeql_v1_0.tar.gz(81 Kbytes)
Manuscript Title: A Maple Package to find First Order Differential Invariants of 2ODEs via a Darboux Approach
Authors: J. Avellar, L.G.S. Duarte, L.A.C.P. da Mota
Program title: FiOrDi
Catalogue identifier: AEQL_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 185(2014)307
Programming language: Maple (release 14).
Computer: PC.
Operating system: Windows 7.
RAM: 128 Mb
Keywords: First integrals, Second order ordinary differential equations, Darboux type approach, Computer algebra.
PACS: 02.30.Hq.
Classification: 4.3, 5.

Nature of problem:
Determination of first order differential invariants for rational second order ordinary differential equations.

Solution method:
The method of solution is based on a Darboux/PS type approach

If, for the ODE under consideration, the Darboux Polynomials are 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 differential first order invariants, 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 associated "D"-operator, the corresponding Darboux polynomails and associated co-factors, etc). In addition, since our package is based on recent theoretical developments [1], it can successfully reduce some rational 2ODEs that were not solved (or reduced) by some of the best-known methods available.

Running time:
This depends strongly on the ODE, but usually under 4 seconds.

[1] L.G.S. Duarte and L.A.C.P. da Mota, Finding Elementary First Integrals for Rational Second Order Ordinary Differential Equations, Journal of Mathematical Physics, Volume 50, Issue 1, pp. 013514-013514-17 (2009)