Function Repository Resource:

ButcherTrees

Get a list of the trees for any Runge-Kutta method of a given order

Contributed by: Wolfram Research

ResourceFunction["ButcherTrees"][p]

gives a list, partitioned by order, of the trees for any Runge–Kutta method of order p.

Details and Options

The trees are represented in a functional form in terms of the elementrary symbol f (\[FormalF]).

Give the trees that are needed for any third-order method:

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Check the trees are all valid syntax using the resource function ButcherTreeQ:

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The resource function ButcherPlot can be used to plot Butcher trees:

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Plot and label the trees through order 5:

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