Midpoint Runge-Kutta (RK2) — second order, two acceleration evaluations.
The state derivative is evaluated at the start of the step and again at the
midpoint of the resulting trajectory; the midpoint derivative advances the
whole step. Exact for constant acceleration. Not symplectic — an undamped
spring loses a little energy per step rather than gaining it.
Midpoint Runge-Kutta (RK2) — second order, two acceleration evaluations.
The state derivative is evaluated at the start of the step and again at the midpoint of the resulting trajectory; the midpoint derivative advances the whole step. Exact for constant acceleration. Not symplectic — an undamped spring loses a little energy per step rather than gaining it.