Integreat`RK`

Integreat`RK`

RKAStable

RKAStable[rk]

returns an algebraic condition equivalent to rk being stable in the left half-plane.

Details and Options

A Runge–Kutta method is I-stable if for all $z in TemplateBox[{}, Complexes]^-$ , where is the linear stability function.
RKAStable returns True or False if the coefficients of rk are NumericQ. If the coefficients contain free variables, RKAStable may return an expression dependent on the free variables.
The following options can be given:
Embedded False whether to use the embedded coefficients

Stage None treat a stage as the solution

DenseOutput False how to evaluate dense output

Examples

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Basic Examples (2)

Determine when a two stage collocation method is A-stable:

An explicit method cannot be A-stable:

Options (3)

Embedded (1)

Check A-stability for an embedded method:

Stage (1)

Check A-stability for a particular stage:

DenseOutput (1)

Check A-stability for the dense output solution:

Tech Notes

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Runge–Kutta Methods