This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)
Numerical Differential Equation Analysis Package
Quadrature Weights and Errors
NewtonCotesWeights, NewtonCotesError Newton-Cotes approximation formula
Runge-Kutta Methods
RungeKuttaOrderConditions list equations for Runge-Kutta methods
ButcherPrincipalError calculate principal error
ButcherQuadratureConditions give quadrature conditions
ButcherColumnConditions, ButcherRowConditions give simplifying conditions
Tree Functions
ButcherPlot plot order condition trees
ButcherTreeQ test for valid syntax
ButcherTrees trees for Runge-Kutta method
ButcherTreeSimplify trees not reduced by assumptions
ButcherTreeCount number of trees
ButcherHeight, ButcherWidth, ButcherOrder characteristics of the tree
ButcherAlpha, ButcherBeta, ButcherBetaBar number of ways of labeling the tree
ButcherGamma density of the tree
ButcherPhi weight of the tree
ButcherSigma order of the symmetry group
Global Settings
$ContinuousExtension whether to generate conditions for continuous extensions
$RungeKuttaMethod type of method to be generated