Wolfram Function Repository
Instant-use add-on functions for the Wolfram Language
Function Repository Resource:
Butcher
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 (1)
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]](https://www.wolframcloud.com/obj/resourcesystem/images/cf9/cf9445c4-ec27-495c-90f3-a23c42dc12c4/305a8a590d13387d.png){kind=small} |
| Out[1]= |  |
Properties and Relations (1)
The non-reduced trees for any order can be obtained using the resource function ButcherTrees:
| In[2]:= | ![ResourceFunction["ButcherTrees"][4]](https://www.wolframcloud.com/obj/resourcesystem/images/cf9/cf9445c4-ec27-495c-90f3-a23c42dc12c4/4194f980761bc8b9.png){kind=small} |
| Out[2]= |  |
Related Links
- Tutorial: Numerical Differential Equation Analysis Package
- Guide: Numerical Differential Equation Analysis Package
- Runge-Kutta Method–Wolfram MathWorld
Version History
- 1.0.0 – 24 September 2019
Related Resources
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License Information
This work is licensed under a Creative Commons Attribution 4.0 International License