RKDispersionOrder[rk]

computes the linear, homogeneous order of dissipation of rk.

Details and Options

  • A Runge–Kutta method has order of dispersion if , where is the dispersion error function.
  • RKDispersionOrder returns an even 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

open allclose all
In[1]:=1
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https://wolfram.com/xid/0d2ctn53wtqioutp85w1fe342q-85a2h7

Basic Examples  (1)Summary of the most common use cases

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

In[1]:=1
✖
https://wolfram.com/xid/0d2ctn53wtqioutp85w1fe342q-vrwsml
Out[1]=1
Out[1]=1

Options  (3)Common values & functionality for each option

Embedded  (1)

Get the order of dispersion for an embedded method:

In[1]:=1
✖
https://wolfram.com/xid/0d2ctn53wtqioutp85w1fe342q-trqub2
Out[1]=1
Out[1]=1

Stage  (1)

Get the order of dispersion for a particular stage:

In[1]:=1
✖
https://wolfram.com/xid/0d2ctn53wtqioutp85w1fe342q-p3gn5m
Out[1]=1
Out[1]=1

DenseOutput  (1)

Get the order of dispersion for the dense output solution:

In[1]:=1
✖
https://wolfram.com/xid/0d2ctn53wtqioutp85w1fe342q-g6bvbr
Out[1]=1
Out[1]=1
Tech Notes
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  • Runge–Kutta Methods