Euler integration
The simplest way to step a simulation forward: add velocity times the timestep to position, one step at a time.
Named for Leonhard Euler (1700s), it's the first thing anyone writes: v += a·Δt; x += v·Δt. Plain "forward" Euler quietly injects energy into the system and sends orbits spiralling outward, so games use semi-implicit (symplectic) Euler — update velocity first, then move with the new velocity. It stays stable for almost no extra work.
When even that drifts, Verlet or RK4 step in. Euler is the textbook example that quietly runs a surprising amount of shipped game physics.