In this video, I introduce one of the most powerful families of numerical integrators: the Runge-Kutta schemes. These provide very accurate and efficient "all-purpose" numerical integrators for ordinary differential equations. Specifically, we introduce the 2nd-order and 4th-order accurate RK schemes (called RK2 and RK4) and break these algorithms down into simple and intuitive steps. These algorithms are also explained with pictures.

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This video was produced at the University of Washington

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0:00 Overview
3:15 2nd Order Runge-Kutta Integrator
8:07 Geometric intuition for RK2 Integrator
19:59 4th Order Runge-Kutta Integrator