Talk:List of Runge–Kutta methods

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I removed the 'citation needed' thingy from the kuttas third order method due to it being correct. Any book on butcher tableaus will prove this right. — Preceding unsigned comment added by 129.12.103.165 (talk) 13:24, 17 October 2011 (UTC)

Formula for 2-stage Lobatto IIIb is incorrect. Change c1=1/2 and c2=1/2 (incorrect) by c1=0 and c2=1

Butcher tableaus for implicit methods

I might be wrong, but could it be, that the definition of $k_{i}$ is not working for implicit methods? The sum doesn't work for $i<2$. 2003:CB:C3EA:CA00:E47F:D884:4654:1E60 (talk) 14:02, 9 July 2017 (UTC)

I agree. Take for instance the backward Euler example under https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods#Implicit_Runge%E2%80%93Kutta_methods. Here, we have $k_{1}=f(t_{n}+h,\ y_{n}+hk_{1})$, but this matches neither the formula for $k_{1}$, i.e. $k_{1}=f(t_{n},\ y_{n})$, nor the general formula for $k_{i}$, which would give $k_{1}=f(t_{n}+h,\ y_{n})$ Andreasdr (talk) 00:38, 9 December 2018 (UTC)

Missing variants

Runge Kutta Butcher

See e.g. [1] —DIV (138.194.12.32 (talk) 00:46, 23 November 2010 (UTC))

Runge-Kutta-Merson

This method is also missing. IRWolfie- (talk) 11:33, 25 February 2011 (UTC)

RK 8 7 (also a D-P method) and Runge-Kutta-Nystrom are missing

I recall hearing that very high order (8/7) is used for very non-stiff problems. http://www.sciencedirect.com/science/article/pii/0771050X81900103

There is also the Runge-Kutta-Nystrom formula http://imajna.oxfordjournals.org/content/7/4/423.short

I was wondering if someone would mind adding these to the page. — Preceding unsigned comment added by 150.135.223.100 (talk) 19:28, 14 November 2012 (UTC)

Fehlberg had multiple methods

The paper is: E. FEHLBERG, Classical Fifth-, Sixth-, Seventh- , and Eighth-Order Runge-Kutta Formulas with Stepsize Control, NASA TR R-287, (1968). It used to be available on the NASA tech reports server, but that is currently down so they can make scientific knowledge into state secrets. Tfr000 (talk) 15:02, 21 April 2013 (UTC)

Summation notation images difficult to read

Several examples use s for the upper bound, but in the rendered image this appears to be indistinguisable from the number 8. Example:

$y_{n+1}=y_{n}+h\sum _{i=1}^{s}b_{i}k_{i}\,$

Is there any way to make this more legible? - Rainwarrior (talk) 22:37, 27 August 2016 (UTC)

bro get glasses 178.19.145.57 (talk) 14:35, 18 November 2023 (UTC)

Check accuracy and references of Diagonally Implicit Runge-Kutta Methods

I noticed that the first DIRK, Kraaijevanger and Spijker's two-stage diagonally implicit, may be incorrect because it's not 2nd-order accurate. (The sums $\sum _{i}b_{i}c_{i}$ and $\sum _{ij}b_{i}a_{ij}$ should both equal 1/2.) Furthermore, despite being linked to specific people, almost none of the DIRKs have citations, either to the original research in which they are proposed or to a textbook compiling and comparing them. JarethHolt (talk) 09:25, 29 July 2020 (UTC)

Picture Repaint Required

Some pictures may be uncorrect in some devices. Negatives may be hidden.

— Preceding unsigned comment added by Nnnn123456789 (talk • contribs) 07:16, 29 December 2020 (UTC)

Three-stage, 3rd order, L-stable Diagonally Implicit Runge–Kutta method:

What is x? It says x=0.4358665215 but I bet x is transcendent. What's the formula? Whoever put it up must know it. 31.17.92.45 (talk) 20:46, 27 January 2024 (UTC)