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

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.

ApartSquareFree[expr] rewrites a rational expression as a sum of terms whose denominators are powers of square-free polynomials. ApartSquareFree[expr, var] treats all ...

First-order PDEs are usually classified as linear, quasi-linear, or nonlinear. The first two types are discussed in this tutorial. A first-order PDE for an unknown function ...

 

ButcherAlpha[tree] gives the number of ways of labeling the vertices of tree with a totally ordered set of labels such that if (m, n) is an edge, then m < n.

ButcherGamma[tree] gives the density of tree.