Integreat`RK`
Integreat`RK`

RKAlgebraicallyStableQ

RKAlgebraicallyStableQ[rk]

returns True if rk is algebraically stable and False, otherwise.

Details and Options

  • A Runge–Kutta method is algebraically stable if and its algebraic stability matrix is positive semi-definite.
  • 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

Basic Examples  (2)

Check if a Radau IIA method is algebraically stable:

An explicit method cannot be A-stable:

Options  (3)

Embedded  (1)

Check algebraic stability for an embedded method:

Stage  (1)

Check algebraic stability for a particular stage:

DenseOutput  (1)

Check algebraic stability for the dense output solution:

Tech Notes
▪
  • Runge–Kutta Methods