This class implements a step interpolator for the 3/8 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/8) [ (8 - 15 θ + 8 θ2) y'1 + 3 * (15 θ - 12 θ2) y'2 + 3 θ y'3 + (-3 θ + 4 θ2) y'4 ] - Using reference point at step end:
y(tn + θ h) = y (tn + h) - (1 - θ) (h/8) [(1 - 7 θ + 8 θ2) y'1 + 3 (1 + θ - 4 θ2) y'2 + 3 (1 + θ) 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 ThreeEighthesIntegrator
@since 1.2