This ordinary differential equations video explains the Improved Euler's method. This numerical method is also known as Heun's method and as a 2nd order Runge Kutta method (RK2). We explain where the formula comes from, based on the average of the two different slopes of the direction field on either side of the interval. We also show how the original Euler's method formula is used inside of this new formula to provide a nicer overall numerical approximation method. We work an example problem using Improved Euler method, and it is the same example that we use in our Euler's method video, so that you can compare and contrast the two methods.
0:00 Where the formula comes from
4:31 Worked example
HMP Euler's Method: https://youtu.be/Atvaac3_NlM
Houston Math Prep Differential Equations Playlist: https://www.youtube.com/playlist?list=PLbYOkEbzW902GJZswbMnWHQaP4kKMS2TV
Houston Math Prep YouTube: https://www.youtube.com/user/HoustonMathPrep