Understanding Fourier Equations in PDE for Beginners

In summary, Fourier trouble in PDE refers to the difficulties that arise when using Fourier analysis techniques to solve partial differential equations. It can be caused by factors such as nonlinearity, boundary conditions, and singularities or discontinuities. To avoid it, careful consideration of boundary conditions and alternative methods may be necessary. Common techniques for dealing with it include using a truncated Fourier series and smoothing or regularization techniques. However, it may not always be possible to completely eliminate Fourier trouble in PDE, but its effects can be minimized with proper techniques.
  • #1
hunter151
35
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.
 
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  • #2
Just out of interest which DKS equation does this refer to ?
 
  • #3
This is the damped kuramoto-sivashinsky equation.
 

FAQ: Understanding Fourier Equations in PDE for Beginners

What is Fourier trouble in PDE?

Fourier trouble in PDE refers to the difficulties that arise when using Fourier analysis techniques to solve partial differential equations (PDEs).

What causes Fourier trouble in PDE?

Fourier trouble in PDE can be caused by various factors such as nonlinearity, boundary conditions, and the presence of singularities or discontinuities.

How can Fourier trouble in PDE be avoided?

To avoid Fourier trouble in PDE, it is important to carefully consider the boundary conditions and the nature of the PDE being solved. In some cases, alternative methods such as spectral methods or finite element methods may be more suitable.

What are some common techniques for dealing with Fourier trouble in PDE?

One common technique for dealing with Fourier trouble in PDE is to use a truncated Fourier series, where only a finite number of terms are included in the solution. Another approach is to use a smoothing or regularization technique to deal with singularities or discontinuities.

Can Fourier trouble in PDE be completely eliminated?

No, it is not always possible to completely eliminate Fourier trouble in PDE, especially in cases where the PDE is highly nonlinear or has complicated boundary conditions. However, careful consideration and appropriate techniques can help to minimize its effects.

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