A187102 Minimum number of function evaluations in each step of an explicit Runge-Kutta method of order n.

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

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..8.

J. C. Butcher, On the attainable Order of Runge-Kutta methods, Math. Comp. 19 (1965) 408-417.

J. C. Butcher, The non-existence of ten stage eighth order explicit Runge-Kutta methods, BIT 25 (1985) 521-540.

A. R. Curtis, An eighth order Runge-Kutta process with eleven function evaluations per step, Numer. Math. 16 (1970) 268-277.

MathOverflow, What is the minimum number of stages s required for a Runge-Kutta type numerical method of given order p?, 2019.

Wikipedia, Runge-Kutta methods.

Formula

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

Crossrefs

Cf. A187103, A087803.

Sequence in context: A339509 A060233 A235203 * A191991 A369138 A257047

Adjacent sequences: A187099 A187100 A187101 * A187103 A187104 A187105

Keyword

hard,more,nonn

Author

Pontus von Brömssen, Mar 04 2011

Status

approved