Wikidata:Property proposal/number of stages

number of stages[edit]

Originally proposed at Wikidata:Property proposal/Natural science

Withdrawn

Description	the number of stages in a Runge-Kutta method
Represents	number of stages (Q97672364)
Data type	Quantity
Domain	item, Runge–Kutta method (Q725944)
Allowed values	1, 2, 3, 4, 5...
Allowed units	none
Example 1	Euler method (Q868454) → 1
Example 2	backward Euler method (Q2736820) → 2
Example 3	Heun's method (Q1531998) → 2
Example 4	Runge–Kutta method (Q725944) → 4

Motivation[edit]

The Runge-Kutta methods are a class of iterative numerical methods used to solve differential equations. The value at the next time-step is given by the following equations

${\begin{aligned}k_{1}&=f\left(t_{n},y_{n}\right)\\k_{2}&=f\left(t_{n}+c_{2}h,y_{n}+h\left(a_{21}k_{1}\right)\right)\\k_{3}&=f\left(t_{n}+c_{3}h,y_{n}+h\left(a_{31}k_{1}+a_{32}k_{2}\right)\right)\\&\vdots \\k_{s}&=f\left(t_{n}+c_{s}h,y_{n}+h\left(a_{s1}k_{1}+a_{s2}k_{2}+\cdots +a_{s,s-1}k_{s-1}\right)\right)\\y_{n+1}&=y_{n}+h\sum _{i=1}^{s}b_{i}k_{i}\end{aligned}}$

where the values of $a_{i},b_{i},c_{i}$ are coefficients that define the particular method. Each equation $k_{i}=...$ is called a stage and the value $s$ is the number of stages. This value is an important characteristic of the method and provides a rough idea of how computationally expensive a given method (and, how accurate it is, if well designed). Therefore, I propose adding a property <number of stages> that would allow us to categorize and search for Runge-Kutta methods based on the number of stages. (See the Wikipedia page [1] for more details.)