Integreat`RK`
Integreat`RK`

RKOrderStarPlot

RKOrderStarPlot[rk]

plots the order star of rk.

RKOrderStarPlot[rk,z]

plots in the square region to .

RKOrderStarPlot[rk,{zmin,zmax}]

plots in a region with corners zmin and zmax.

Details and Options

  • The order star of rk is the set of z in TemplateBox[{}, Complexes] for which the modulus of RKLinearStability[rk,z] is greater than the modulus of .
  • RKOrderStarPlot has the same options as ComplexRegionPlot with the following additions:
  • 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)

Plot the order star of the classical fourth order Runge–Kutta method:

Since the region is symmetric about the real axis, we can focus on the upper half:

Style an order star:

Options  (3)

Embedded  (1)

Plot the order star of an embedded method:

Stage  (1)

Plot the order star of a particular stage:

DenseOutput  (1)

Plot the order star of the dense output solution at the step midpoint:

Tech Notes
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  • Runge–Kutta Methods