Very good explanation! I love doing physics simulations, but usually drown myself in words whilst reading about solving differential equations numerically. Thank you very much!
A very promising introduction! This might become my favorite channel. Especially thanks for knowing beforehand what questions arise and exhaustively answer them
You have a great way of explaining what for most of us would be quite difficult mathematics 😄 please start writing books about physics and math,I would certainly buy it👍
That was a great explanation. As someone that doesn't work anywhere near this field, I always wondered how it was done. What a powerful tool. Subscribed and may the RUclips algorithm bless you by recommending it to others.
Awesome introduction. Please keep them coming! Would gladly support a patreon. You break this down expertly and still make it pleasantly entertaining. Thanks!
Excellent first video; looking forward to the series! Not sure how deep into hardware you're hoping to get with your PhD, but I would love to hear about what opportunities you see for different computing architectures (GPUs, TPUs, ..., FPGAs, ASICs) to accelerate CFD. GPUs seem to be promising but I'm sure there's some nuance to it when it comes to scaling or maybe the methods that can be used. Same with FPGAs. But I really hope that not too far in the future some accessible software/hardware system will exist that can compute reasonably accurate real-time fluid simulations at the scale of a Cessna. One day right :)
We differential algebraists have worked on solving nonlinear systems of PDEs and ODEs for a century now, starting with the work of Joseph Fels Ritt, who is my PhD dissertation grandfather (my thesis advisor Dr Richard Cohn's advisor was Ritt) We have had ten international conferences: DART: Differential Algebra & Related Topics, starting in 2000, Rutgers, Newark when I first attended, through DART X in February 2020, CUNY: City University of New York. I am still stuck on an unsolved conjecture from my PhD thesis that was formulated in April 1999. I am using a lot of Python + Sympy programming to help me figure it out. But, it is overload for my computer: the computation on even the smallest nontrivial example is too hard for my computer to handle. I really need a supercomputer to write it out. In the meantime, I attack the problem from all sorts of other angles, purely algebraically.
8:23 I have a question about this part (sorry if it's obvious), but don't we still have to know what y'_n is to figure out y'_(n+1), since y'_n is present in both equations?
The computer generated photos are: 1. right, 2. right, 3. right. I am pretty sure of this, because as far as I can remember, the hubble telescope photos had lots of red in them
Come from Reddit. You did a great job for introducing people to this amazing world :)
yeah me too
Please don't stop making this series
Very good explanation! I love doing physics simulations, but usually drown myself in words whilst reading about solving differential equations numerically. Thank you very much!
A very promising introduction! This might become my favorite channel. Especially thanks for knowing beforehand what questions arise and exhaustively answer them
You have a great way of explaining what for most of us would be quite difficult mathematics 😄 please start writing books about physics and math,I would certainly buy it👍
I really regret not finding this channel during my PDE course. You explained it very well, thank you!
That was a great explanation. As someone that doesn't work anywhere near this field, I always wondered how it was done. What a powerful tool.
Subscribed and may the RUclips algorithm bless you by recommending it to others.
I wish Numerical Analysis was more popular on RUclips. This stuff is so cool! Btw, what did you use to animate the graphs?
Nothing special, just saved the plotted figure at different times then threw it together using ffmpeg afterwards
Great video! You are really adding to the golden age of physics content on yt. Love the topic and the humor!
i am here from reddit and i dont regret . time used best.
Amazing explanation! Loved numerical analysis at college.
Awesome introduction. Please keep them coming! Would gladly support a patreon. You break this down expertly and still make it pleasantly entertaining. Thanks!
Excellent first video; looking forward to the series! Not sure how deep into hardware you're hoping to get with your PhD, but I would love to hear about what opportunities you see for different computing architectures (GPUs, TPUs, ..., FPGAs, ASICs) to accelerate CFD. GPUs seem to be promising but I'm sure there's some nuance to it when it comes to scaling or maybe the methods that can be used. Same with FPGAs. But I really hope that not too far in the future some accessible software/hardware system will exist that can compute reasonably accurate real-time fluid simulations at the scale of a Cessna. One day right :)
Nice presentation !
We differential algebraists have worked on solving nonlinear systems of PDEs and ODEs for a century now, starting with the work of Joseph Fels Ritt, who is my PhD dissertation grandfather (my thesis advisor Dr Richard Cohn's advisor was Ritt)
We have had ten international conferences: DART: Differential Algebra & Related Topics, starting in 2000, Rutgers, Newark when I first attended, through DART X in February 2020, CUNY: City University of New York.
I am still stuck on an unsolved conjecture from my PhD thesis that was formulated in April 1999.
I am using a lot of Python + Sympy programming to help me figure it out. But, it is overload for my computer: the computation on even the smallest nontrivial example is too hard for my computer to handle. I really need a supercomputer to write it out.
In the meantime, I attack the problem from all sorts of other angles, purely algebraically.
8:23 I have a question about this part (sorry if it's obvious), but don't we still have to know what y'_n is to figure out y'_(n+1), since y'_n is present in both equations?
Great content, waiting for more!
The mass spring equation, did you made is correct? I see no f=ma.. kinldy tell howmit appears.
The computer generated photos are: 1. right, 2. right, 3. right. I am pretty sure of this, because as far as I can remember, the hubble telescope photos had lots of red in them
Wow good stuff
Very entertaining
Man thanks. This is great.
I actually found it more stable to use the updated version of y'' too so y'_(n+1)=y'_n + h * y''_(n+1)
Please explain the Algorithms to solve Navier Stokes equations.
4:03 I actually did, watcha gonna do about it?
Alright thats it give me your parents' numbers I'm calling them
@@BeyondtheBigBang jokes on you, I don’t know my parents, hahaha…ha…ha…eehhhh…
Haha…ha… oooooo hmmm rip
Thank you Sir, I subscribed lol
I love you too! How u doing? Just checking..