Wikidata:Property proposal/Butcher tableau

Butcher tableau[edit]

Originally proposed at Wikidata:Property proposal/Natural science

Done: Butcher tableau (P8558) (Talk and documentation)

Description	a table containing the coefficients of a Runge-Kutta method
Represents	Runge–Kutta method (Q725944)
Data type	Mathematical expression
Example 1	backward Euler method (Q2736820) → ${\begin{array}{l\|l}1&1\\\hline &1\end{array}}$
Example 2	explicit Runge–Kutta method (Q51846055) → ${\begin{array}{r\|lllll}0&&&&&\\c_{2}&a_{21}&&&\\c_{3}&a_{31}&a_{32}&&\\\vdots &\vdots &&\ddots &\\c_{s}&a_{s1}&a_{s2}&\cdots &a_{s,s-1}\\\hline &b_{1}&b_{2}&\cdots &b_{s-1}&b_{s}\end{array}}$
Example 3	Ralston's method (Q51879118) → ${\begin{array}{l\|l}0&\\2/3&2/3\\\hline &1/4\end{array}}$
Planned use	add property to the existing Runge-Kutta method items.
See also	defining formula (P2534)

Motivation[edit]

In mathematics, the Runge-Kutta methods are an important class of numerical methods for solving differential equations. Each method is defined by a set of coefficients that are arranged into a table called the Butcher tableau. Creating this property would allow each method to be tied to its tableau. Currently, on Wikipedia, the Butcher tableau for each Runge-Kutta method cannot be found in a consistent place on each page--sometimes not all. Adding a property would facilitate the creation of an infobox.

Making this property distinct from defining formula (P2534) is desirable because each Runge-Kutta method can also be written out as a set of equations that should be the defining formula (P2534) (cf. Euler method (Q868454)) The-erinaceous-one (talk) 06:36, 25 July 2020 (UTC)[reply]

See also discussion here --★ → A ir on 90 08:06, 26 July 2020 (UTC)[reply]

Discussion[edit]

Notified participants of WikiProject Mathematics

Oppose There is no need to create a too specific property, although Butcher tableau could be considered as a Wikidata-ically "identifier". defining formula (P2534) IMHO suffices. The problem was that adding tables in LaTeX on Wikidata is not easy, not the creation of a new property. One could already either insert on Wikidata the entire Butcher tableau as formula with applies to part (P518) Butcher tableau (Q51846190) as qualifier or insert on Wikidata the matrix A and vectors b and c with applies to part (P518) Runge-Kutta matrix (Q97664752), Runge-Kutta weights vector (Q97664754), Runge-Kutta nodes vector (Q97664755) respectively as qualifier --★ → A ir on 90 08:06, 26 July 2020 (UTC)[reply]
- @Airon90: One problem with defining formula (P2534) is that it has single-best-value constraint (Q52060874). If we want to include the Butcher table and the equations in the form $y_{n+1}=y_{n}+h\sum _{i=1}^{s}b_{i}k_{i}$ then we would violate the constraint. This problem becomes more pronounced if we were to use Runge-Kutta matrix (Q97664752), Runge-Kutta weights vector (Q97664754), Runge-Kutta nodes vector (Q97664755). That being said, I think it is worthwhile to somehow include Runge-Kutta matrix (Q97664752), Runge-Kutta weights vector (Q97664754), Runge-Kutta nodes vector (Q97664755) because I might, for example, want to compare all the b-vectors for various Runga-Kutta methods. The-erinaceous-one (talk) 22:31, 27 July 2020 (UTC)[reply]
Support I don't think defining formula (P2534) is correct, the tableau does not "define" the method, it specifies coefficients for it, but the method itself is an iterative transformation. ArthurPSmith (talk) 14:51, 27 July 2020 (UTC)[reply]
- Though I'm wondering, how many items in Wikidata could this possibly apply to? ArthurPSmith (talk) 18:04, 28 July 2020 (UTC)[reply]
- @ArthurPSmith: The current number of Runge-Kutta methods in Wikidata is five, or so, but the number of Runge-Kutta methods listed on Wikipedia[1]. includes over thirty methods. A quick search finds that there are RK methods not included in Wikipedia's list[2].
Support I would like have this property created so that I can start importing Runge-Kutta methods from [3] into Wikidata. Without the proposed Butcher tableau property, adding meaningful distinguishing information to each method items is difficult. – The preceding unsigned comment was added by The-erinaceous-one (talk • contribs) at 21:12, August 2, 2020‎ (UTC). (proposer).