Integreat`RK`
Integreat`RK`

RKCompose

RKCompose[{{rk1,w1},{rk2,w2},…}]

composes rk1, rk2, … with steps sizes scaled by w1, w2, …, respectively.

RKCompose[{rk1,rk2,…}]

creates a Runge–Kutta method from a step of rk1, rk2, … in sequence.

rk1[rk2]

composes a step of rk1 with a step of rk2.

rk^p

composes p steps of rk with step size h/p.

Details and Options

  • Runge–Kutta methods are closed under composition, i.e., applying a Runge–Kutta method to the solution produced by another.
  • RKCompose[{rk1,rk2,…}] is equivalent to RKCompose[{{rk1,1},{rk2,1},…}].
  • rk^p is equivalent to RKCompose[{{rk,1/p},…,{rk,1/p}}].

Examples

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Basic Examples  (2)

Compose three methods with different step sizes:

Two half steps of an embedded pair:

Properties & Relations  (1)

Composition removes dense output:

Tech Notes
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  • Runge–Kutta Methods