Integreat`RK`
Integreat`RK`

RKDissipationOrder

RKDissipationOrder[rk]

computes the linear, homogeneous order of dissipation of rk.

Details and Options

  • A Runge–Kutta method has order of dissipation if , where is the dissipation error function.
  • RKDissipationOrder returns an odd integer or ∞.
  • The following options can be given:
  • EmbeddedFalsewhether to use the embedded coefficients
    StageNonetreat a stage as the solution
    DenseOutputFalsehow to evaluate dense output

Examples

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Basic Examples  (2)

Get the order of dissipation of the classical fourth order Runge–Kutta method:

A symmetric method has no dissipation error:

Options  (3)

Embedded  (1)

Get the order of dissipation for an embedded method:

Stage  (1)

Get the order of dissipation for a particular stage:

DenseOutput  (1)

Get the order of dissipation for the dense output solution:

Tech Notes
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  • Runge–Kutta Methods