Error Estimation in Numerical Methods

This lecture covers the estimation of errors in numerical methods for solving ordinary differential equations. It discusses the concepts of local truncation error, consistency, stability, and convergence. The instructor explains how to calculate the error expressions and the importance of Lipschitz continuity in ensuring stability. The lecture also delves into the progressive Euler scheme, transported truncation error, and the total calculation error. Emphasis is placed on understanding the relationship between error estimation and the accuracy of numerical solutions.