Differential Algebra
rif
The Rif package can be used for the simplification of overdetermined ODE and PDE systems. It is the successor of the Standard Form
project, and has the following additional features:
1.Computation with nonlinear systems.
2.Advanced case splitting capablilities for discovery of particular solution branches with desired properties.
3.A visualization tool for examination of the binary tree that results from multiple cases.
4.Algorithms for working with formal power series solutions of the system.
Further information: http://www.cecm.sfu.ca/~wittkopf/rif.html
Indiff
Description: A MAPLE package for overdetermined differential systems with Lie symmetry.
Author: Elizabeth Mansfield
Further information: http://www.ukc.ac.uk/ims/maths/people/E.L.Mansfield.html
Online demo: Coming soon...
diffalg
Description: The diffalg package is a collection of routines to handle systems of polynomial differential equations and inequations. The functionalities include differential elimination, expansion of the solutions into formal power series and analysis of singular solutions. The underlying theory and terminology belongs to differential algebra.
Author: François Boulier , Evelyne Hubert
Further information: http://www-sop.inria.fr/cafe/Evelyne.Hubert/webdiffalg/
diffgrob2
Description: A MAPLE package to simplify overdetermined systems of nonlinear differential equations of polynomial type
Author: Elizabeth Mansfield
Further information: http://www.ukc.ac.uk/ims/maths/people/E.L.Mansfield.html
Online demo: http://centaur.maths.qmw.ac.uk/CATHODE/DiffGrob2_demo.html
Symmetry
LieSym
Description: Lie-point symmetry computations of systems of differential equations
Author: Willy Hereman
Further information: http://www.mines.edu/fs_home/whereman/liesym.html
DimSym
Description: Symmetry Determination and Linear Differential Equation Package
Author: James Sherring
Further information: http://www.latrobe.edu.au/www/mathstats/Maths/Dimsym/
LIE and BIGLIE
Description: Programs to find Lie symmetries of differential equations
Author: Alan Head
Further information: http://www.cmst.csiro.au/LIE/LIE.htm
DESOLV
Description: A Maple program for the determination of Lie Symmetries of differential equations.
Author: J. Carminati, Khai Vu
Further information: http://www.cm.deakin.edu.au/research/jcarm/desolv.htm
LiePDE
Description: Computation of point, contact and higher order
symmetries of single and systems of differential equations
Author: Thomas Wolf
Further information: ftp://lie.math.brocku.ca/twolf/crack
ApplySym
Description: For given symmetries it computes symmetry and
similarity variables and transforms differential equations
to these new variables
Author: Thomas Wolf
Further information: ftp://lie.math.brocku.ca/twolf/crack
Differential Geometry
VESSIOT
Designed to assist researchers in geometric methods in differential equations.The software package Vessiot contains commands for all the basic operations of calculus on jetspaces.
Further information: http://math.usu.edu/~fg_mp/Pages/SymbolicsPage/Symbolics.html
Vecalc
Description: For doing algebraic and differential calculations with symbolic vector
functions (not matrices) in curvilinear coordinates
Author: Edgardo Cheb-Terrab
Further information: http://lie.uwaterloo.ca/ecterrab/software.htm
Grassmann
Description: For symbolic computing with anti-commutative and non-commutative variables
Author: Edgardo Cheb-Terrab
Further information: http://lie.uwaterloo.ca/ecterrab/software.htm
PDEtools
Description: For the analytical solving of Partial Differential Equations
Author: Edgardo Cheb-Terrab
Further information: http://lie.uwaterloo.ca/ecterrab/software.htm
ODEtools
Description: For solving Ordinary Differential Equations using classification, integrating factor and symmetry methods.
Author: Edgardo Cheb-Terrab
Further information: http://lie.uwaterloo.ca/ecterrab/software.htm
partials
Description: For evaluating partial and functional derivatives of (and with respect to) tensor functions
Author: Edgardo Cheb-Terrab
Further information: http://lie.uwaterloo.ca/ecterrab/software.htm