RKAlgebraicStabilityMatrix[rk]

computes the algebraic stability matrix of rk.

Details and Options

  • The algebraic stability matrix of a Runge–Kutta method has entries for .
  • 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/0f9a6o34noktse6seq3emqm75z0y-3dmyuy

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

The algebraic stability matrix of the classical fourth order Runge–Kutta method:

In[1]:=1
✖
https://wolfram.com/xid/0f9a6o34noktse6seq3emqm75z0y-iyo3uj
Out[1]=1

Options  (3)Common values & functionality for each option

Embedded  (1)

Get the algebraic stability matrix for an embedded method:

In[1]:=1
✖
https://wolfram.com/xid/0f9a6o34noktse6seq3emqm75z0y-21czf2
Out[1]=1

Stage  (1)

Get the algebraic stability matrix associated with a particular stage:

In[1]:=1
✖
https://wolfram.com/xid/0f9a6o34noktse6seq3emqm75z0y-3j40a7
Out[1]=1

DenseOutput  (1)

Get the algebraic stability matrix for the dense output solution:

In[1]:=1
✖
https://wolfram.com/xid/0f9a6o34noktse6seq3emqm75z0y-1dis2c
Out[1]=1
Tech Notes
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  • Runge–Kutta Methods