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

Author

Pontus von Brömssen, Mar 04 2011

Keywords

• hard
• more
• nonn

Comments

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

Links

• 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.

Crossrefs

Cf. A187103, A087803.

Formula

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