Error Estimation in Numerical Methods

This lecture covers the estimation of errors in numerical methods for solving ordinary differential equations. Starting with the concept of local truncation error, the instructor explains the importance of consistency, stability, and convergence in numerical methods. The lecture delves into the progressive Euler scheme, discussing how errors accumulate and affect the accuracy of solutions. Various numerical methods such as Heun, modified Euler, and classic Runge-Kutta are explored, emphasizing the impact of errors on stability and solution accuracy. Through practical exercises, students learn to implement and analyze different resolution methods, gaining insights into error estimation and solution stability.