Crank-Nicolson and Heun's Methods

This lecture covers the Crank-Nicolson and Heun's methods, discussing the uniqueness of Cauchy problem solutions and truncation errors. The lecture delves into the iterative process of solving non-linear equations at each time step, emphasizing the implicit nature of Crank-Nicolson's method. It also explores the role of Newton iterations and the corresponding Newton interations. The lecture further explains the concept of trapezoidal rule and its application in implicit methods. Additionally, it touches upon the significance of local truncation error and the convergence of numerical methods. The lecture concludes with an analysis of global truncation error and the importance of accuracy in approximating solutions.