Digital Physics: Convergence and Error Analysis

This lecture covers the evaluation feedback from the fall 2021 course, where students express their opinions on the course content, exercises, and assistance provided. The instructor discusses the order of convergence, error analysis, and the implementation of adaptive time steps in numerical simulations. The lecture emphasizes the importance of understanding convergence and error estimation in numerical methods, particularly in the context of physics simulations. Various examples and exercises are used to illustrate the concepts, including the application of Runge-Kutta methods and the analysis of error propagation. The lecture concludes with a comparison between fixed and adaptive time steps, highlighting the efficiency and accuracy gained by using adaptive schemes.