Integreat`RK`
Integreat`RK`

RKEPolynomial

RKEPolynomial[rk, y]

evaluates the E-polynomial, which is used to assess A-stability, of rk at y.

Details and Options

  • The E-polynomial of a Runge–Kutta method is , where and are the numerator and denominator of the linear stability function, respectively.
  • The polynomial generated by RKEPolynomial is even and has real coefficients.
  • 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 E-polynomial of a collocation method:

Options  (3)

Embedded  (1)

Get E-polynomial of an embedded method:

Stage  (1)

Evaluate the E-polynomial for a particular stages

DenseOutput  (1)

Get the E-polynomial of the dense output solution:

Properties & Relations  (1)

The E-polynomial can be expressed in terms of the numerator and denominator of the linear stability function:

Tech Notes
▪
  • Runge–Kutta Methods