A187103 Maximum order of an explicit Runge-Kutta method with n function evaluations in each step.

1, 2, 3, 4, 4, 5, 6, 6, 7, 7, 8

Offset

1,2

Comments

a(n) <= n-3 for n >= 10 (Butcher 1985).

Observation: first 10 terms coincide with A303735. - Omar E. Pol, Oct 04 2018

The preceding observation (by Omar E. Pol) holds also for the 11th term. - Pontus von Brömssen, Apr 05 2023

Links

Table of n, a(n) for n=1..11.

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

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) = max{k; A187102(k)<=n}.

Crossrefs

Cf. A087803, A187102, A303735.

Sequence in context: A354459 A089058 A282717 * A303735 A080444 A082288

Adjacent sequences: A187100 A187101 A187102 * A187104 A187105 A187106

Keyword

hard,more,nonn

Author

Pontus von Brömssen, Mar 04 2011

Status

approved