Wolfram Research

Function Repository Resource:

ButcherTreeSimplify

Source Notebook

Get the butcher trees through a given order that are not reduced by Butcher’s quadrature or row- or column-simplifying conditions

Contributed by: Wolfram Research

ResourceFunction["ButcherTreeSimplify"][p,η,ξ]

gives the set of trees through order p that are not reduced by Butcher's quadrature conditions through order p, row-simplifying conditions through order η or column-simplifying conditions through order ξ.

Details and Options

The result is grouped by order, starting with the first nonvanishing tree.

Examples

Basic Examples

Get the additional trees that are necessary for a fourth-order method, assuming that the quadrature conditions through order 4 and the row and column simplifying assumptions of order 1 hold:

In[1]:=
ResourceFunction["ButcherTreeSimplify"][4, 1, 1]
Out[1]=

Properties and Relations

The non-reduced trees for any order can be obtained using ButcherTrees:

In[2]:=
ResourceFunction["ButcherTrees"][4]
Out[2]=

Resource History

Related Resources

License Information