95 research outputs found
Computer Algebra Solving of Second Order ODEs Using Symmetry Methods
An update of the ODEtools Maple package, for the analytical solving of 1st
and 2nd order ODEs using Lie group symmetry methods, is presented. The set of
routines includes an ODE-solver and user-level commands realizing most of the
relevant steps of the symmetry scheme. The package also includes commands for
testing the returned results, and for classifying 1st and 2nd order ODEs.Comment: 24 pages, LaTeX, Soft-package (On-Line help) and sample MapleV
sessions available at: http://dft.if.uerj.br/odetools.htm or
http://lie.uwaterloo.ca/odetools.ht
Computer Algebra Solving of First Order ODEs Using Symmetry Methods
A set of Maple V R.3/4 computer algebra routines for the analytical solving
of 1st. order ODEs, using Lie group symmetry methods, is presented. The set of
commands includes a 1st. order ODE-solver and routines for, among other things:
the explicit determination of the coefficients of the infinitesimal symmetry
generator; the construction of the most general invariant 1st. order ODE under
given symmetries; the determination of the canonical coordinates of the
underlying invariant group; and the testing of the returned results.Comment: 14 pages, LaTeX, submitted to Computer Physics Communications.
Soft-package (On-Line Help) and sample MapleV session available at:
http://dft.if.uerj.br/symbcomp.htm or ftp://dft.if.uerj.br/pdetool
Integrating factors for second order ODEs
A systematic algorithm for building integrating factors of the form mu(x,y),
mu(x,y') or mu(y,y') for second order ODEs is presented. The algorithm can
determine the existence and explicit form of the integrating factors themselves
without solving any differential equations, except for a linear ODE in one
subcase of the mu(x,y) problem. Examples of ODEs not having point symmetries
are shown to be solvable using this algorithm. The scheme was implemented in
Maple, in the framework of the "ODEtools" package and its ODE-solver. A
comparison between this implementation and other computer algebra ODE-solvers
in tackling non-linear examples from Kamke's book is shown.Comment: 21 pages - original version submitted Nov/1997. Related Maple
programs for finding integrating factors together with the ODEtools package
(versions for MapleV R4 and MapleV R5) are available at
http://lie.uwaterloo.ca/odetools.ht
- …