I think we assume that the boundaries are periodic for exactly that reason. Also curious if something like this would be possible for other types of boundary conditions.
by definition, solving in the frequency domain would give you the solution of an unbound problem. The solution with boundary conditions use Green's function. You can FT the Green's function related to your BC, do point-wise multiplication with your initial function transformed, and then apply inverse FT. Here the FT is only use to compute the convolution of Green's function with your initial function. You could use Laplace transform, but FT is faster.
If you want to employ FFT for the Coupled HJB PDEs that does not have a fixed type (hyperbolic, parabolic), what would the best way forward? I have encountered such PDEs in the non-cooperative Differential Game forms.
I need to adapt fourier- derived equations for my construction of an alternate number base for a mathematical subsystem system of a linear koopman complex dimension transformation with an infinite domain and range but I'm not really sure how to do that since this is all in vector forms and springs, ect, while mine has a vector eigenvalue for each function in a plain.... it's a bit beyond taught my maths to actually invent a new series of equations to assist in complex plain analysis of numbers which are random or not analytical in the "real" number plain.. I need to find some resources for creating equations in an imaginary plain for complex number problems without solutions in real domains. any suggestions?
Why don’t you try converting linear koopman complex dimension transformation into complex plain and then do the Fourier analysis on top of Laplace transformations to construct easy alternate number base. After that it would we way easier to continue. Best of luck.
![Solving PDEs with the FFT, Part 2 [Matlab]](http://i.ytimg.com/vi/RilggJd1_LY/mqdefault.jpg)
Greatly appreciated for making these videos! I have a PhD degree yet these are some of the best lectures I ever had.
spectacular explanation !!!.please make a video on linear prediction for noise elimination using python
Prof. Brunton, how do you dealias the convolution term in Python? Do we not need to do dealiasing in the Burgers equation? Thank you.
The FFT really implements circular convolution. How would you apply "edge" conditions in an FFT-based solver for the wave equation?
I think we assume that the boundaries are periodic for exactly that reason. Also curious if something like this would be possible for other types of boundary conditions.
by definition, solving in the frequency domain would give you the solution of an unbound problem. The solution with boundary conditions use Green's function. You can FT the Green's function related to your BC, do point-wise multiplication with your initial function transformed, and then apply inverse FT. Here the FT is only use to compute the convolution of Green's function with your initial function. You could use Laplace transform, but FT is faster.
I'll try this out!
Is there a place to copy the code and mess around with it for slightly different problems?
If you want to employ FFT for the Coupled HJB PDEs that does not have a fixed type (hyperbolic, parabolic), what would the best way forward? I have encountered such PDEs in the non-cooperative Differential Game forms.
Just great Professor Brunton, thank you. Can you do some videos on "Proper Generalized Decomposition" method for PDE's on python or matlab?
thank you.
I need to adapt fourier- derived equations for my construction of an alternate number base for a mathematical subsystem system of a linear koopman complex dimension transformation with an infinite domain and range but I'm not really sure how to do that since this is all in vector forms and springs, ect, while mine has a vector eigenvalue for each function in a plain.... it's a bit beyond taught my maths to actually invent a new series of equations to assist in complex plain analysis of numbers which are random or not analytical in the "real" number plain.. I need to find some resources for creating equations in an imaginary plain for complex number problems without solutions in real domains. any suggestions?
Why don’t you try converting linear koopman complex dimension transformation into complex plain and then do the Fourier analysis on top of Laplace transformations to construct easy alternate number base. After that it would we way easier to continue. Best of luck.