PROGRAM SUMMARY
Title of program:
PSsolver
Catalogue identifier:
ADPR
Ref. in CPC:
144(2002)46
Distribution format: tar gzip file
Operating system: Linux (RedHat 6.2,Debian 2.0/2.2),Windows(95/98)
High speed store required:
32MK words
Number of lines in distributed program, including test data, etc:
2970
Keywords:
First order ordinary differential equations (FOODEs),
Symbolic computation, Prelle-Singer procedure, Liouvillian and
elementary functions, General purpose.
Programming language used: Maple V Release 5
Computer:
Pentium-II, 350 MHz .
Nature of physical problem:
Symbolic solution of first order differential equations via the
Prelle-Singer method.
Method of solution:
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.
Typical 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.
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.
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.