Numerical Methods for ODEs: Crank-Nicolson, Heun, Euler, RK4

This lecture covers various numerical methods for solving ordinary differential equations, including the Crank-Nicolson method, Heun method, modified Euler method, and the classic Runge-Kutta method. The instructor explains the concepts behind each method, such as implicitness, predictor-corrector approaches, and error estimation techniques. The lecture also delves into the importance of truncation errors, local and transported errors, and the convergence of numerical methods. Practical examples and code implementations are provided to illustrate the application of these methods in solving ODEs.