RK4 (Runge–Kutta)
A fourth-order integrator that samples acceleration four times per step and blends them — far more accurate than Euler for the same timestep.
Fourth-order Runge–Kutta (Carl Runge and Wilhelm Kutta, around 1900) evaluates the derivative four times across a step — one at the start, two in the middle, one at the end — and blends them so the error shrinks with the fourth power of the step size. For the same Δt it's far more accurate than Euler, which is why orbital and vehicle simulations reach for it.
The catches: four force evaluations per step, and it isn't symplectic, so energy can still drift over long runs. Glenn Fiedler's "Integration Basics" put it on every game developer's radar — yet many still pick semi-implicit Euler or Verlet for the better cost-to-stability ratio.