Euler Backward Method: ODEs

This lecture covers the Euler backward method for solving ordinary differential equations (ODEs). It explains how to approximate the derivative at a given point using backward finite differences, leading to a nonlinear system that needs to be solved. The stability of the method is discussed, showing that it is insensitive to the step size. An example is provided to illustrate the application of the Euler backward method, demonstrating how the error decreases with each step. A comparison between explicit and implicit methods is also presented.