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Instant-use add-on functions for the Wolfram Language
Function Repository Resource:
Butcher
Get a list of terms in the Taylor series expansion of the error for Runge–Kutta methods
Contributed by:
Wolfram Research
ResourceFunction["ButcherPrincipalError"][p,s] gives the principal error for a method of order p with s stages. | |
ResourceFunction["ButcherPrincipalError"][p] gives the principal error using stage-independent tensor notation. |
Details and Options
The principal error for a method of order p is a list of the order p+1 terms appearing in the Taylor series expansion of the error.
The following options can be given:
| "ContinuousExtension" | False | whether to generate conditions for continuous extensions |
| "RungeKuttaMethod" | "Implicit" | type of Runge-Kutta method |
Valid settings for "RungeKuttaMethod" are "DiagonallyImplicit", "Explicit", and "Implicit".
Examples
Basic Examples (2)
The principal error coefficients for any second‐order, s‐stage method:
| In[1]:= | ![ResourceFunction["ButcherPrincipalError"][2, s]](https://www.wolframcloud.com/obj/resourcesystem/images/812/812b1c59-1dbd-4024-b964-e8fe9827f644/53f3b042fc91a7b1.png){kind=small} |
| Out[1]= |  |
The same coefficients in the stage-independent notation:
| In[2]:= | ![ResourceFunction["ButcherPrincipalError"][2]](https://www.wolframcloud.com/obj/resourcesystem/images/812/812b1c59-1dbd-4024-b964-e8fe9827f644/23cd77eaba1aa960.png){kind=small} |
| Out[2]= |  |
Related Links
- Tutorial: Numerical Differential Equation Analysis Package
- Guide: Numerical Differential Equation Analysis Package
Version History
- 1.0.0 – 04 November 2019
Related Resources
Related Symbols
License Information
This work is licensed under a Creative Commons Attribution 4.0 International License