Wolfram Function Repository
Instant-use add-on functions for the Wolfram Language
Function Repository Resource:
Butcher
Get a list of the number of Butcher trees through a given order
Contributed by:
Wolfram Research
ResourceFunction["ButcherTreeCount"][p] gives a list of the number of trees through order p. |
Examples
Basic Examples (1)
Determine the number of trees at each order through order 10:
| In[1]:= | ![ResourceFunction["ButcherTreeCount"][10]](https://www.wolframcloud.com/obj/resourcesystem/images/177/177af9f4-3bef-43ea-99cb-ed157c348d8e/0f735340847724f6.png){kind=small} |
| Out[1]= |  |
Scope (1)
The result of ButcherTreeCount can be used to calculate the total number of trees required at each order:
| In[2]:= | ![ResourceFunction["ButcherTreeCount"][10] // Accumulate](https://www.wolframcloud.com/obj/resourcesystem/images/177/177af9f4-3bef-43ea-99cb-ed157c348d8e/3078b8e5cbbbcf92.png){kind=small} |
| Out[2]= |  |
Properties and Relations (1)
The result is equivalent to evaluating the length of each output of the resource function RungeKuttaOrderConditions at each level, but the calculation is more efficient:
| In[3]:= | ![RepeatedTiming[ResourceFunction["ButcherTreeCount"][10]]](https://www.wolframcloud.com/obj/resourcesystem/images/177/177af9f4-3bef-43ea-99cb-ed157c348d8e/0599b72049285f2f.png){kind=small} |
| Out[3]= |  |
| In[4]:= | ![RepeatedTiming[
Length /@ ResourceFunction["RungeKuttaOrderConditions"][10]]](https://www.wolframcloud.com/obj/resourcesystem/images/177/177af9f4-3bef-43ea-99cb-ed157c348d8e/4ef7f37fc51e34d5.png){kind=small} |
| Out[4]= |  |
Related Links
- Tutorial: Numerical Differential Equation Analysis Package
- Guide: Numerical Differential Equation Analysis Package
- Runge-Kutta Method–Wolfram Mathworld
- Wikipedia–Butcher group
Version History
- 1.0.0 – 03 September 2019
Related Resources
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License Information
This work is licensed under a Creative Commons Attribution 4.0 International License