Beautiful illustrations of using FFT to solve pde! I understand that this is an elementary example so things are kept simple. However, solving heat equations with ode45, which uses explicit time stepping scheme, is unstable since heat equations are stiff. It will be great to point it out so people will turn to the correct scheme later when they really need it.
@@var67 I think it has to be a little joke. I found a website with this image which suggests he's left handed and they mirror the image. cdn.geekwire.com/wp-content/uploads/2020/11/brunton2-630x420.jpg Thanks for the great videos, Steve! Watched the entire series so far.
Beautiful content. I wanted so much to pursue a PhD in applied math at UMN in this direction, unfortunately two days ago my application got rejected. This is so painful !
@@mokranemokrane1941 Nice! I think you are already lucky to live in France and have access to high quality education (while on USA you need to pay high fees for probably the same education??). Anyway, you can guess my country? it is called the "middle of nowhere".
What should we do if we want to consider boundary conditions for the problem? like ux(left,t)=ux(right,t) uxx(left,t)=uxx(right,t) or ux(left,t)=ux(right,t)=f(x)
Hi Prof. Brunton, really appreciates your great demo in this video! I tried another initial condition (step function) for this method, and it showed some errors at the edge. I think it might due to lack of boundary condition. Will you talk more about how to put boundary restriction into the code? Thanks!
Great lecture! what if the original singnal is complex number, the second derivative operator needs to use FFT for real part and imaginary part, respectively？
Dear Prof. Brunton, Great lecture! I found a very minor typo in 'rhsHeat' function. => duhatdt = -a^2*(kappa.^2).' .* uhat; (maybe ignored because kappa.^2 would be a vector including the absolute values.)
Thanks for this. I'm using Octave instead of Matlab so it was giving me issues, not sure if this was one of them. I also changed a few things in the code to make it plot, like instead of plotting the waterfall with u(1:10:end,:)) I plotted real(u(1:10:end,:)) and got the same plot in his book.
Great video Eigen Steve! But I am curious as to where the formulation written on line 9 is coming from? I understood the description, but I'm just confused as to how / where this came from? What about the 'fft' function in MATLAB, why is this not used instead of what's currently on line 9? - Forgive me, if I'm off base... new to Mr Fourier.
![Solving PDEs with the FFT [Python]](http://i.ytimg.com/vi/hDeARtZdq-U/mqdefault.jpg)
![Solving PDEs with the FFT [Python]](/img/tr.png)
you have Spoiled us Dr. Brunton! implementations in both Pyhton and Matlab!
What about Julia?
Beautiful illustrations of using FFT to solve pde! I understand that this is an elementary example so things are kept simple. However, solving heat equations with ode45, which uses explicit time stepping scheme, is unstable since heat equations are stiff. It will be great to point it out so people will turn to the correct scheme later when they really need it.
Thank you for separate Pthon and Matlab videos!
My fav topic. And great thanks to Prof. Brunton for making these videos.
Thank you very much
your lectures are really interesting with your straightforward explanation
I am loving your FFT. Very basic and informative. I am waiting and looking forward when you will explain more about Non-uniform Fourier transform.
Awesome! Thank you!
Thank you.
This is very valuable knowledge. Thanks for sharing it.
I thought you were writing normally and then mirrored the video. 🤔
@@var67 I agree .. he seems either bored with all the mirrored video questions ..... or really enjoying it.
Me too. May be his years teaching gave him this super power.
He was writing in the time domain instead of the frequency domain
@@var67 I think it has to be a little joke. I found a website with this image which suggests he's left handed and they mirror the image. cdn.geekwire.com/wp-content/uploads/2020/11/brunton2-630x420.jpg
Thanks for the great videos, Steve! Watched the entire series so far.
@@speedengineering How many people wear their wedding ring on their right hand? 😉😉
Thank you, Steve this was fascinating for me. Just I couldn't find the end of the code from the Movie to the end. Best
Beautiful content. I wanted so much to pursue a PhD in applied math at UMN in this direction, unfortunately two days ago my application got rejected. This is so painful !
I'm so sorry to hear that. But keep learning!
Where do you live?
@@AEX-rk4lg France
@@mokranemokrane1941 Nice! I think you are already lucky to live in France and have access to high quality education (while on USA you need to pay high fees for probably the same education??). Anyway, you can guess my country? it is called the "middle of nowhere".
Thanks for this high quality content
Hello Prof. Brunton,
Do you not mirror the video?
Thanks for all your videos!
What should we do if we want to consider boundary conditions for the problem?
like
ux(left,t)=ux(right,t)
uxx(left,t)=uxx(right,t)
or
ux(left,t)=ux(right,t)=f(x)
Hi Prof. Brunton, really appreciates your great demo in this video! I tried another initial condition (step function) for this method, and it showed some errors at the edge. I think it might due to lack of boundary condition. Will you talk more about how to put boundary restriction into the code? Thanks!
Hi late reply, but I believe it’s due to the fact we need it to be periodic, so a step function can only be done if you step it down further along
Dr Steve when you transformed uxx to frequency domain, you put kappa square but when you transformed ut to frequency you didn't write w along with it?
Great lecture! what if the original singnal is complex number, the second derivative operator needs to use FFT for real part and imaginary part, respectively？
Dear Prof. Brunton, Great lecture! I found a very minor typo in 'rhsHeat' function. => duhatdt = -a^2*(kappa.^2).' .* uhat; (maybe ignored because kappa.^2 would be a vector including the absolute values.)
Thanks for this. I'm using Octave instead of Matlab so it was giving me issues, not sure if this was one of them. I also changed a few things in the code to make it plot, like instead of plotting the waterfall with u(1:10:end,:)) I plotted real(u(1:10:end,:)) and got the same plot in his book.
0:30 wait, are you actually writing backwards for these?? I thought you just flipped the video horizontally 🤣
Great contents as always.
Great video Eigen Steve! But I am curious as to where the formulation written on line 9 is coming from? I understood the description, but I'm just confused as to how / where this came from? What about the 'fft' function in MATLAB, why is this not used instead of what's currently on line 9? - Forgive me, if I'm off base... new to Mr Fourier.
Nice way to confuse the audience who really were trying to figure out how this board works, hahaha
Wow great content there!
curious... are you writing in reverse or the video get flipped?
Fantastic!
Wow! Subscribed!
So you just write everything mirrored?!?
A key observation is that he is always is pulling his tshirt down.
I feel really intelligent being a high schooler here, which year do students learn this?