6.2.2-Numerical Integration: Romberg Integration and Richardson's Extrapolation

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.

[mechwarreir]

Oh my god you explained this soooo much better than my boring engineer teacher. He took 2 hours of taylor series crap and missed the whole point. Props, and thanks!

[davidboozer]

At about 4:20, it should be pointed out he DOUBLED the number of function evaluations. The way he said it in the video sounded like he only needed 2 more evaluations to go from O(h2) to O(h4). It's a true statement provided you've only taken 2 evaluations to start with, but it's better to be more general when teaching.

[SunFilmsProduction]

4:49 General Romberg formula should have I(j+1), (k-1) not I(j+1), (k+1) as written in the video

[tomiadventures]

Yes, as Jacob mentioned in a comment below, it should be k-1 instead of k+1 (around 4:30-5:30 time mark).

[qsdfcvgyjmkl]

At 5:10, the first integration of the general equation is supposed to be I_(j+1, k-1), not I_(j+1, k+1)

[chrainy]

not clear w.r.t I_{j, k}. You did not explain what I_{j, k} is so it is difficult to understand the table.

[SEBA]

thanks for the lessons, it's helping me a lot. What do j and k stand for in the general Romberg algorithm?

[rafaelortega]

Thank you for the video. I think you should explain in depth the meaning of the subindexes. I figured it out after a few minutes and the comments confirmed my suspicions but I think that would improve dramatically the understanding of the video. Anyhow, thank you very much.

[umutsim]

Thanks for the video. I have one comment on the audio quality. I think you should lower the treble of your recordings, it's a little bit disturbing if you watch the video with a headphone.

[jafarmat]

i think your general formula is At 4:29 you formula says something like this : I(1, 2) = [ 4 I(2, 1) - I(1, 1) ] / 3, there is no  I(1, 2), maybe you mean I(2, 2), because we're moving forward in the algorithm :)

[Exorcisto]

Thank you so much you that was really helpful

[palashkhanra]

5:58, sir what is the name of that book ?