Testwiki:Property proposal/number of stages

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Motivation

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

$\begin{array}{cc}{k}_1& =f(t_n,y_n)\\ k_2& =f(t_n+c_{2}h,y_n+h\left(a_{21}{k}_1\right))\\ k_3& =f(t_n+c_{3}h,y_n+h(a_{31}{k}_1+a_{32}{k}_2))\\ & ⋮\\ k_s& =f(t_n+c_{s}h,y_n+h(a_{s1}{k}_1+a_{s2}{k}_2+\cdots +a_{s,s-1}{k}_{s-1}))\\ y_{n+1}& =y_n+h\sum _{i=1}^s{b}_i{k}_i\end{array}$

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.)

The-erinaceous-one (talk) 07:16, 28 July 2020 (UTC)

Discussion

Template:O I am withdrawing the property proposal because the number of stages can be modeled without a new property by Template:Statement