This class implements a step interpolator for the Gill fourth order Runge-Kutta integrator.
This interpolator allows to compute dense output inside the last step computed. The interpolation equation is consistent with the integration scheme :
- Using reference point at step start:
y(tn + θ h) = y (tn) + θ (h/6) [ (6 - 9 θ + 4 θ2) y'1 + ( 6 θ - 4 θ2) ((1-1/√2) y'2 + (1+1/√2)) y'3) + ( - 3 θ + 4 θ2) y'4 ] - Using reference point at step start:
y(tn + θ h) = y (tn + h) - (1 - θ) (h/6) [ (1 - 5 θ + 4 θ2) y'1 + (2 + 2 θ - 4 θ2) ((1-1/√2) y'2 + (1+1/√2)) y'3) + (1 + θ + 4 θ2) y'4 ]
where θ belongs to [0 ; 1] and where y'
1 to y'
4 are the four evaluations of the derivatives already computed during the step.
@see GillIntegrator
@since 1.2