Is Helmholtz equation a Poisson Equation?

In summary, the Helmholtz equation and Poisson's equation are both second order PDEs, but the latter is more general as the function f can be any value, while in the Helmholtz equation, f is equal to -ku. The separation of variables method can be used to solve certain types of the Helmholtz equation. While they have similarities, one is not a subset or form of the other.
  • #1
5,697
238
Helmholtz equation:##\nabla^2 u=-ku## is the same form of ##\nabla^2 u=f##.

So is helmholtz equation a form of Poisson Equation?
 
Physics news on Phys.org
  • #2
They're both second order PDEs, but the Poisson f is a more general function, not necessarily related to the unknown function u. If the function f is 0, then the Poisson equation reduces to the Laplace equation.

In the solution of certain types of the Helmholtz equation, the separation of variables can be utilized.

http://en.wikipedia.org/wiki/Helmholtz_equation

http://en.wikipedia.org/wiki/Poisson's_equation

The generality of 'f' in Poisson's equation makes it trickier to solve than Laplace.
 
  • #3
Thanks for the reply, I understand the difference between the two. But Helmholtz is also in form of Poisson, only when ##f=-ku##. So, can I say Helmholtz is a subset or one form of Poission Equation?

Thanks
 
Last edited:
  • #4
yungman said:
Thanks for the reply, I understand the difference between the two. But Helmholtz is also in form of Poisson, only when ##f=-k\nabla^2 u##. So, can I say Helmholtz is a subset or one form of Poission Equation?

Thanks

I think you mean when f = -ku

FWIW, sure, go ahead.
 
  • #5
SteamKing said:
I think you mean when f = -ku

FWIW, sure, go ahead.

Yes, my bad. What is FWIW?

Thanks
 
  • #6
FWIW = For What It's Worth
 
  • Like
Likes 1 person
  • #7
Leaving the chat speak aside, generally speaking the only connection between Poisson's equation and Helmholtz equation is that they are both elliptic 2nd order linear PDEs. One is not a particular case of the other, as posts 2 and especially 3,4 above insinuate.
 
  • #8
Thanks everyone.
 

Suggested for: Is Helmholtz equation a Poisson Equation?

Replies
11
Views
1K
Replies
1
Views
1K
Replies
12
Views
2K
Replies
1
Views
747
Replies
3
Views
1K
Replies
2
Views
486
Replies
3
Views
727
Back
Top