RKLinearStabilityPlot[rk]

plots the linear stability region of rk.

RKLinearStabilityPlot[rk,z]

plots in the square region to .

RKLinearStabilityPlot[rk,{zmin,zmax}]

plots in a region with corners zmin and zmax.

Details and Options

  • The stability region of rk is the set of z in TemplateBox[{}, Complexes] for which the modulus of RKLinearStability[rk,z] is less than or equal to one.
  • RKLinearStabilityPlot 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)Summary of the most common use cases

Plot the linear stability region 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 a stability plot:

Options  (3)Common values & functionality for each option

Embedded  (1)

Plot the stability region of an embedded method:

Plot the primary and embedded regions together:

Stage  (1)

Plot the linear stability region of a particular stage:

DenseOutput  (1)

Plot the stability region of the dense output solution at the step midpoint:

Tech Notes
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  • Runge–Kutta Methods