Talk:Dormand–Prince method

There are even higher order RK methods attributed to Dormand and Prince

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) 19:27, 14 November 2012 (UTC)

Is mentioned at Runge–Kutta methods#Runge–Kutta–Nyström methods, otherwise Be bold. Regards 17387349L8764 (talk) 11:00, 24 August 2023 (UTC)

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At the end of the second paragraph, it says: "For this reason, the Dormand–Prince method is more suitable when the higher-order solution is used to continue the integration, a practice known as local interpolation (Hairer, Nørsett & Wanner 1993)." But my 2008 copy of the same book (corrected 3rd printing) calls it "local EXTRAPOLATION"! I'm changing it, correct me if you have better information than my own (and if you do, explain why,please!) Regards, Jose Brox The Article says, "The difference between these solutions is then taken to be the error of the (fourth-order) solution". This seems to be an odd statement. As the article later explains, Dormand-Prince is optimized for the fifth-order solution to be as accurate as possible. Thus the fifth-order solution will be used in further computations, and so the computed difference is more reasonable explained as an estimate for the fifth-order solution, and not the fourth-order one.141.44.27.69 (talk) 15:47, 9 February 2011 (UTC) _____________________________________ Just below the Butcher table the article says "The first row of b coefficients gives the fourth-order accurate solution..." It should be the other way around: The first row of b coefficients gives the fifth-order accurate solution .... Regards, Alex Dragt http://www.physics.umd.edu/dsat ______________________________________________ — Preceding unsigned comment added by 71.205.94.74 (talk) 01:56, 27 February 2012 (UTC)

Last edited at 02:56, 28 February 2012 (UTC). Substituted at 02:01, 5 May 2016 (UTC)

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Clarifications

What does "embedded" mean in this context? 159.162.102.250 (talk) 06:56, 21 April 2022 (UTC)

The original paper is from the 1980s, right now it is sorted as part of Runge–Kutta methods#Adaptive Runge–Kutta methods if that helps. Regards 17387349L8764 (talk) 10:59, 24 August 2023 (UTC)