Sequential impulse
Erin Catto's iterative physics solver, which nudges the bodies' velocities one contact at a time until every constraint is roughly satisfied.
Rather than assembling and solving one big system for all contacts at once, the method takes a single contact at a time, computes the impulse that contact needs, applies it and moves on. A full sweep over all contacts repeats a few times per step — mathematically a Gauss–Seidel relaxation.
Catto introduced it around 2006 and built Box2D around it. It is easy to implement, cache-friendly and easy to warm-start, which made it the de facto standard for 2D and lighter 3D physics. The catch is that it is approximate: more iterations give stiffer but never perfect contacts.