These videos were created to accompany a university course, Numerical Methods for Engineers, taught Spring 2013. The text used in the course was "Numerical Methods for Engineers, 6th ed." by Steven Chapra and Raymond Canale.
Thanks a million, your videos have really helped me... if it wasn't for them I wouldn't be getting through this subject! You have to acknowledge, guys, very few people have uploaded a whole set of videos on the very complicated subject of Numerical Methods, even though there's a few mistakes!
I know the video is 3 years old but basically you are just explaining euler's formula in the first part. And the function/2 part 2:39 is actually Heun's Method? You should have explained that in the first part of the video instead of saying it in Euler's. Throughout the whole video the only Heun's method i saw was the title. It might be easier to use Yo,Y1,Y2,Y3. Anyways thanks, I kind of understand.
Not quite. This is in fact just Heun's Method. Heun's method is a predictor-corrector method. The first part (up to about 2:39) is the predictor. The second part is the corrector. This is not an explanation but an example. The explanation is in video 7.1.4 of this same series/playlist. Both the predictor and corrector are necessary for it to be Heun's Method. Both use Euler's concept that y_i+1 = y_i + slope*h, but the estimation of the slope is slightly different in each case, and second part (the corrector) uses the result from the first (the predictor). As for notation, in an effort to be consistent and minimize confusion, I use the same notation as the textbook. I hope this helps.
nice effort, but all of this work is for first order equations, which we can solve at the first place with laplace. i watched the series from the beginning waiting for you to get to higher order equations or non-linear equations =\ anyway, no matter what, your noble effort is appreciated
Late response, but...a higher-order differential equation can be re-written as a coupled system of first-order equations, and solved using the methods shown here. Non-linear equations are a different animal altogether and you essentially need to consider each flavor of non-linearity separately.
