Classical Runge-Kutta (RK4) — fourth order, four acceleration evaluations.
§38's recommendation for "small, smooth engineering demonstrations where
accuracy matters more than cost". Exact for constant acceleration, and
accurate to O(dt⁴) on smooth systems; like every explicit RK method it is
not symplectic, so an undamped spring decays very slowly over long runs.
k1…k4 below are the four (velocity, acceleration) derivative samples of
the standard tableau; the position slopes kNx are the velocities of the
evaluation points.
Classical Runge-Kutta (RK4) — fourth order, four acceleration evaluations.
§38's recommendation for "small, smooth engineering demonstrations where accuracy matters more than cost". Exact for constant acceleration, and accurate to
O(dt⁴)on smooth systems; like every explicit RK method it is not symplectic, so an undamped spring decays very slowly over long runs.k1…k4below are the four(velocity, acceleration)derivative samples of the standard tableau; the position slopeskNxare the velocities of the evaluation points.