ButcherQuadratureConditions[p, s] gives the quadrature conditions up to and including order p for s stages. ButcherQuadratureConditions[p] gives the quadrature conditions in ...

ButcherRowConditions[p, s] gives the row-simplifying conditions up to and including order p for s stages. ButcherRowConditions[p] gives the row-simplifying conditions in ...

ButcherRowSum is an option to RungeKuttaOrderConditions that specifies whether the row\[Dash]sum conditions for the \[FormalC]_i should be added to the list of order ...

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

ButcherSimplify is an option to RungeKuttaOrderConditions that specifies whether to apply Butcher's row- and column-simplifying conditions.

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.

ButcherTreeSimplify[p, \[Eta], \[Xi]] gives the set of trees through order p that are not reduced by Butcher's quadrature conditions through order p, row-simplifying ...

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.