Talk:List of Runge–Kutta methods

	This article is within the scope of WikiProject Lists, an attempt to structure and organize all list pages on Wikipedia. If you wish to help, please visit the project page, where you can join the project and/or contribute to the discussion.ListsWikipedia:WikiProject ListsTemplate:WikiProject ListsList articles
???	This article has not yet received a rating on the project's importance scale.

Mathematics Low‑priority

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles
Low	This article has been rated as Low-priority on the project's priority scale.

Untitled

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)[reply]

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)[reply]

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)[reply]

Missing variants

Runge Kutta Butcher

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

Runge-Kutta-Merson

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

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)[reply]

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)[reply]

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)[reply]

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

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)[reply]

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)[reply]

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)[reply]