Understanding Fourier Equations in PDE for Beginners

  • Thread starter Thread starter hunter151
  • Start date Start date
  • Tags Tags
    Fourier Pde
hunter151
Messages
35
Reaction score
0
So I suppose my Fourier knowledge is a little bit rusty. Any help would be greatly appreciated.

http://pmgz.net/3259.jpg

How do they get from the original DKS equation to the Fourier space DKS equation (from eq 1 to eq 2)?

Thanks greatly for any help.
 
Physics news on Phys.org
Just out of interest which DKS equation does this refer to ?
 
This is the damped kuramoto-sivashinsky equation.
 

Thread 'Volterra equation of the second kind'

There is the following linear Volterra equation of the second kind $$ y(x)+\int_{0}^{x} K(x-s) y(s)\,{\rm d}s = 1 $$ with kernel $$ K(x-s) = 1 - 4 \sum_{n=1}^{\infty} \dfrac{1}{\lambda_n^2} e^{-\beta \lambda_n^2 (x-s)} $$ where $y(0)=1$, $\beta>0$ and $\lambda_n$ is the $n$-th positive root of the equation $J_0(x)=0$ (here $n$ is a natural number that numbers these positive roots in the order of increasing their values), $J_0(x)$ is the Bessel function of the first kind of zero order. I...
View full post »

Thread 'Visual Representation of Separation of Varables'

Are there any good visualization tutorials, written or video, that show graphically how separation of variables works? I particularly have the time-independent Schrodinger Equation in mind. There are hundreds of demonstrations out there which essentially distill to copies of one another. However I am trying to visualize in my mind how this process looks graphically - for example plotting t on one axis and x on the other for f(x,t). I have seen other good visual representations of...
View full post »

Similar threads

I Stuck on solving a non homogenous (linear) PDE
Replies
36
Views
4K
A Partial differential equation containing the Inverse Laplacian Operator
Replies
3
Views
3K
A Understanding dummy variable in solution of 1D heat equation
Replies
6
Views
2K
Solving the 3D Diffusion Equation with Fourier Spectral Techniques
Replies
2
Views
2K
I PDE - Heat Equation - Cylindrical Coordinates.
Replies
3
Views
4K
B Why the Fourier series doesn't work to solve any differential equation?
Replies
11
Views
5K
Numerical method for wave equation
Replies
2
Views
2K
A discussion about Fourier and Laplace transforms and calculus
Replies
4
Views
3K
I Physics? Setting up PDE for air resistance at high velocity
Replies
2
Views
2K
A direct proof involving a positive summability kernel
Replies
7
Views
1K

Hot Threads

Recent Insights

Back
Top