Ordinary Differential Equations: Methods and Accuracy

This lecture covers the basics of ordinary differential equations, starting with the general form and the momentum definition. It then introduces the Euler method for solving initial value problems, discussing its accuracy and limitations. The Taylor method is presented as a more accurate alternative, followed by multistep methods and implicit methods. Results from applying these methods are shown, comparing the exact solution with the approximations obtained. The lecture concludes with a discussion on the accuracy of the different methods and the implications for solving differential equations.