Wen Shen, Penn State University. Lectures are based on my book: "An Introduction to Numerical Computation", published by World Scientific, 2016. See promo video: • Book Promo: An Introdu...
Пікірлер: 35
@mahmoudzorkot11504 жыл бұрын
Thanks alot Prof. Shen.. the best explanation i ever got
@deashehu25918 жыл бұрын
You lady are amazing! Thanks for sharing !
@wenshenpsu8 жыл бұрын
+Dea Shehu I am glad that you liked it.
@pansy04126 жыл бұрын
really great lecture, thank you for sharing!
@wenshenpsu6 жыл бұрын
Thanks for watching.
@user-gr4zb5he4f6 жыл бұрын
It's really helpful. Thank you!
@wenshenpsu6 жыл бұрын
Cheers and have a great day.
@athassawatkammanee22296 жыл бұрын
Very good teaching. Thank your very much.
@wenshenpsu6 жыл бұрын
Thanks!
@Edifier12218 жыл бұрын
One of your best videos, really interesting! I wish you where my professor :/
@wenshenpsu8 жыл бұрын
+KirkElPozz Thanks for the comments. Happy viewing!
@oghenefejiroakpodamure77888 жыл бұрын
how can i implement the IMEX METHOD. i need your help
@deepa74336 жыл бұрын
Could you please explain x_(n+1) = x_n + h*[ b_n*f_n + ...] how h appears in this step at 13:20? I undertsand b_n is the integral of l_n(t) but how is the h factored out from all the integrals?
@oghenefejiroakpodamure77888 жыл бұрын
VERY GOOD LECTURE. CHEERS
@wenshenpsu8 жыл бұрын
+cauchy god swill Thanks.
@murraycoumbis26214 жыл бұрын
at 17:22, i did the integral and got something slightly different to that which is written. as i can tell, fn-1 should be (fn-1)/2. please correct me if i am wrong but i just want to be sure
@murraycoumbis26214 жыл бұрын
i answered my own question by cross referencing with your other video and i was correct. for reference, see kzfaq.info/get/bejne/ep-kmZRyt8-6Zqs.html at 2:30
@francescosarnari71588 жыл бұрын
Hi Wen, lectures are just amazing, so clear and instructive! Thank you! Listen, I have a couple of questions for you: what can we say in terms of the numerical stability of the AB-Moulton method? Does the numerical stability and/or the efficiency of this numerical methos depend on its order, i.e. on how many steps backwards I consider to predict the new one? Thank you so much, and I look forward to your reply. Cheers, Francesco
@wenshenpsu8 жыл бұрын
+Francesco Sarnari Stability of multistep method is not covered in this course that I taught. The stability depends on two factors: (1) the choice of the starting values must be consistent; (2) if the underlining system is stiff, then it will impose a restriction on the size of the time step. You should read some more advanced text on numerical methods for ODEs to get all the details.
@francescosarnari71588 жыл бұрын
+wenshenpsu Thank you very much for you reply, Wen. Based on your experience, could you give me the reference of a text which you consider to be particularly good to learn about stability of multispet methods? Cheers, Francesco
@wenshenpsu8 жыл бұрын
+Francesco Sarnari It seems that the book by John Butcher, titled "Numerical Methods for Ordinary differential Equations", has some discussion on this in Chapter 4. However, I have not read the book myself, so I can't promise anything. Good luck.
@sierraschellenberg27177 жыл бұрын
please show an example of ABM
@Edifier12218 жыл бұрын
I don't understand at 42:59 when you propose to use AB2 for calculate X1, this method requires 2 previous points but we only have one (Xo, which is given). Thanks :)
@wenshenpsu8 жыл бұрын
+KirkElPozz The best one might be Heun's method, which has the same order.
@paneersingh7 жыл бұрын
U are looking beautiful + u cleared my doubts.
@wenshenpsu7 жыл бұрын
Thanks for watching!
@oghenefejiroakpodamure77888 жыл бұрын
thanks
@wenshenpsu8 жыл бұрын
+cauchy god swill You are welcome.
@abderrahimwakif92408 жыл бұрын
thank you doctor from morocco
@wenshenpsu8 жыл бұрын
+abderrahim waif Thanks!
@devins94027 жыл бұрын
读文献的时候,看到fractional calculus的linear multistep methods,没读懂。然后去整数阶,结果发现很像改进欧拉法,心中还是有不清晰的地方。直到看到您的视频,非常清晰易懂!// When I reading literature about linear multistep methods of fractional differential equations, I found I am confused. So I went back to common fractional differential equations and still not totally understand, but found that this method to some extent like improved Euler method. Until I watch your open math course, I think I understand it totally! Thank you for recording this video and wish your book a bestseller among students.
@wenshenpsu7 жыл бұрын
Thanks.
@emmanuelnthala53966 жыл бұрын
Wen, I like your classes so much. They are very easy to follow, your writing I very legible and you make numerical analysis a beautiful endeavor. However as I've commented in some of your past videos, the one who films you does injustice to the followers of your youtubes. He or she does not follow you when you move back and forth to make refer to points you already listed on the board. I believe you can fix this. Otherwise continue enlightening the world!
@wenshenpsu6 жыл бұрын
Thanks for your comments. I will try to make HD videos in the future.
@emmanuelnthala53966 жыл бұрын
Dr. Wen, can you share with me active research focus in numerical analysis taking place now? If possible please let me know articles I can read in connection to the research areas you'll advise. My email is nthaco@gmail.com