Function Repository Resource:

# ButcherPlot

Plot order condition trees for Runge-Kutta method

Contributed by: Wolfram Research
 ResourceFunction["ButcherPlot"][tree] gives a plot of the Butcher tree tree. ResourceFunction["ButcherPlot"][{tree1,tree2,…}] gives an array of plots of the treei.

## Details and Options

Rooted trees in ResourceFunction["ButcherPlot"][] correspond to the elementary differentials appearing in the Taylor expansion of the system of differential equations, and branching of a sub-tree corresponds to exponentiation in the differential equation.
In Butcher plots, roots are denoted by circles and the number of vertices in a tree correspond to the order of the tree.
The following options can be given:
 "ButcherPlotColumns" Automatic number of columns in an array of plots "ButcherPlotNodeSize" 1 scaling factor for the nodes in the trees "ButcherPlotRootSize" 1 scaling factor for highlighting roots "ButcherPlotLabel" {} list of plot labels

## Examples

### Basic Examples (2)

Use the resource function ButcherTrees to generate trees for any Runge-Kutta method of order 3:

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Plot the trees:

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### Scope (2)

Plot a Butcher tree:

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Generate several trees with the resource function ButcherTrees and use ButcherPlot to plot them:

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### Options (4)

#### ButcherPlotColumns (1)

Plot trees in a single column:

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#### ButcherPlotNodeSize (1)

Increase the size of nodes:

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#### ButcherPlotNodeSize (1)

Highlight roots with larger circles:

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#### ButcherPlotLabel (1)

Label trees:

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## Version History

• 1.0.0 – 04 November 2019