Quadrature Weights and Errors

NewtonCotesWeights, NewtonCotesError — Newton–Cotes approximation formula

GaussianQuadratureWeights, GaussianQuadratureError — Gaussian 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