Improved Solvers: Runge-Kutta Methods

This lecture discusses the concept of improving error estimation in numerical methods by avoiding the need for higher order derivatives. It explores the use of Runge-Kutta methods to estimate functions at multiple points within an interval, combining them to achieve a better estimate. The lecture delves into the geometric interpretation of a second-order Runge-Kutta method, demonstrating how it predicts and corrects points by averaging slopes. By implementing this predictor-corrector approach, the method provides a more precise solution compared to simpler methods like Euler forward.