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[Licence| Download | New Version Template] adpr_v1_0.tar.gz(32 Kbytes)
Manuscript Title: An extension of the Prelle-Singer method and a Maple implementation.
Authors: L.G.S. Duarte, S.E.S. Duarte, L.A.C.P. da Mota, J.E.F. Skea
Program title: PSsolver
Catalogue identifier: ADPR_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 144(2002)46
Programming language: Maple V Release 5.
Computer: Pentium-II, 350 MHz.
Operating system: Linux (RedHat 6.2/Debian 2.0/Debian 2.2), Windows(95/98).
RAM: 32M words
Keywords: First order ordinary differential equations (FOODEs), Symbolic computation, Prelle-Singer procedure, Liouvillian and elementary functions, General purpose.
Classification: 4.3.

Nature of problem:
Symbolic solution of first order differential equations via the Prelle-Singer method.

Solution method:
The method of solution is based on the standard Prelle-Singer method, with extensions for the cases when the FOODE contains elementary functions. Additionally, an extension of our own which solves FOODEs with a sub class of (non-elementary) Liouvillian functions is included.

Restrictions:
If the integrating factor for the FOODE under consideration has factors of high degree in the dependent and independent variables and in the elementary functions appearing in the FOODE, the package may spend a long time to find the solution. Also, when dealing with FOODEs containing elementary functions, it is essential that the algebraic dependency between them is recognized. If that does not happen, our program can miss some solutions.

Unusual features:
Our implementation of the Prelle-Singer approach not only solves FOODEs, but can also be used as a research tool that allows the user to follow all the steps of the procedure. For example the eigenpolynomials associated with the FOODE (see section 4) can be calculated. In addition, our package is successful in solving FOODEs that were not solved by some of the most commonly available solvers. Finally, our package implements a theoretical extension (for details, see section 3 and [1, 2]) to the original Prelle-Singer approach that enhances its scope, allowing it to tackle some FOODEs whose solutions involve non-elementary functions.

Running time:
This depends strongly on the FOODE, but usually under 2 seconds, and almost always under 30 seconds. These times were obtained using a Pentium-II, 350 MHz, with 64 MB RAM.

References:
[1] M. Singer, Liouvillian First Integrals of Differential Equations Trans. Amer. Math. Soc., 333 673-688 (1992).
[2] L.G.S. Duarte, S.E.S. Duarte, L.A.C.P. da Mota and J.E.F. Skea, Tackling FOODEs with Liouvillian Solutions within the PS-procedure, submitted to J. Phys. A: Mathematical, Nuclear and General.