Numerical Differential Equation Analysis Package

Quadrature Weights and Errors

NewtonCotesWeights, NewtonCotesError NewtonCotes approximation formula

GaussianQuadratureWeights, GaussianQuadratureError Gaussian formula

RungeKutta Methods

RungeKuttaOrderConditions list equations for RungeKutta 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 RungeKutta 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