A187102 - OEIS

%I #14 Apr 10 2023 10:51:17

%S 1,2,3,4,6,7,9,11

%N Minimum number of function evaluations in each step of an explicit Runge-Kutta method of order n.

%C a(n)>=n+3 for n>=8 (Butcher 1985).

%H J. C. Butcher, <a href="https://doi.org/10.1090/S0025-5718-1965-0179943-X">On the attainable Order of Runge-Kutta methods</a>, Math. Comp. 19 (1965) 408-417.

%H J. C. Butcher, <a href="https://doi.org/10.1007/BF01935372">The non-existence of ten stage eighth order explicit Runge-Kutta methods</a>, BIT 25 (1985) 521-540.

%H A. R. Curtis, <a href="https://doi.org/10.1007/BF02219778">An eighth order Runge-Kutta process with eleven function evaluations per step</a>, Numer. Math. 16 (1970) 268-277.

%H MathOverflow, <a href="https://mathoverflow.net/questions/339041/what-is-the-minimum-number-of-stages-s-required-for-a-runge-kutta-type-numeric">What is the minimum number of stages s required for a Runge-Kutta type numerical method of given order p?</a>, 2019.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods">Runge-Kutta methods</a>.

%F a(n) = min{k; A187103(k)=n}.

%Y Cf. A187103, A087803.

%K hard,more,nonn

%O 1,2

%A _Pontus von Brömssen_, Mar 04 2011