ButcherHeight[tree] gives the height of tree.

ButcherOrder[tree] gives the number of vertices in tree.

ButcherSigma[tree] gives the order of the symmetry group of isomorphisms of tree with itself.

ButcherTreeCount[p] gives a list of the number of trees through order p.

ButcherTreeQ[tree] gives True if tree is a valid Butcher tree, and False otherwise.

ButcherTrees[p] gives a list, partitioned by order, of the trees for any Runge\[Dash]Kutta method of order p.

ButcherWidth[tree] gives the width of tree.

$ContinuousExtension is a global environment setting, specifying whether to generate conditions for continuous extensions of Runge\[Dash]Kutta methods.

$RungeKuttaMethod is a global environment setting, specifying the type of method to be generated by ButcherPhi and related functions.

The general form of an ODE with order n is As in the case of second-order ODEs, such an ODE can be classified as linear or nonlinear. The general form of a linear ODE of ...