Programs in Physics & Physical Chemistry
|[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).|
|Operating system: Windows 7.|
|RAM: 128 Mb|
|Keywords: First integrals, Second order ordinary differential equations, Darboux type approach, Computer algebra.|
|Classification: 4.3, 5.|
Nature of problem:
Determination of first order differential invariants for rational second order ordinary differential equations.
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.
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 , it can successfully reduce some rational 2ODEs that were not solved (or reduced) by some of the best-known methods available.
This depends strongly on the ODE, but usually under 4 seconds.
|||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)|
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