Integreat`RK`
Integreat`RK`

RKDispersionError

RKDispersionError[rk,ν]

evaluates the linear, homogeneous dissipation error of rk at ν.

Details and Options

  • The dispersion error function of a Runge–Kutta method is , where is the linear stability function.
  • When a Runge–Kutta method is applied to the oscillatory test problem , the solution satisfies where .
  • 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  (1)

Get the dispersion error of the classical fourth order Runge–Kutta method:

Options  (3)

Embedded  (1)

Evaluate the dispersion error for an embedded method:

Stage  (1)

Get the dispersion error for a particular stage:

DenseOutput  (1)

Get the dispersion error for the dense output solution:

Tech Notes
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  • Runge–Kutta Methods