This class implements a step interpolator for the classical 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) (y'2 + y'3) + ( -3 θ + 4 θ2) y'4 ] - Using reference point at step end:
y(tn + θ h) = y (tn + h) + (1 - θ) (h/6) [ (-4 θ^2 + 5 θ - 1) y'1 +(4 θ^2 - 2 θ - 2) (y'2 + y'3) -(4 θ^2 + θ + 1) 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 ClassicalRungeKuttaIntegrator
@since 1.2