Function Repository Resource:

ButcherPhi

Compute the weight of a Butcher tree

Contributed by: Wolfram Research

ResourceFunction["ButcherPhi"][tree,s]

gives the weight of tree in an s-stage Runge-Kutta method.

ResourceFunction["ButcherPhi"][tree]

gives the weight of tree in stage-independent tensor notation.

Details and Options

The weight of tree is the left-hand side of the order conditions imposed by tree.

The following option can be given:

"RungeKuttaMethod"

"Implicit"

type of Runge-Kutta method

Valid settings for "RungeKuttaMethod" are "DiagonallyImplicit", "Explicit" and "Implicit".

Compute the elementary weight function imposed by f[f[f[f]f^2]] for an s‐stage method:

In[1]:=

$ResourceFunction[ "ButcherPhi"][\[FormalF][\[FormalF][\[FormalF][\[FormalF]] \[FormalF]^2]], s]$

Out[1]=

Repeat, giving the result in stage-independent tensor notation:

In[2]:=

$ResourceFunction[ "ButcherPhi"][\[FormalF][\[FormalF][\[FormalF][\[FormalF]] \[FormalF]^2]]]$

Out[2]=