Is Helmholtz equation a Poisson Equation?

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  • #1
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Helmholtz equation:##\nabla^2 u=-ku## is the same form of ##\nabla^2 u=f##.

So is helmholtz equation a form of Poisson Equation?
 

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  • #2
SteamKing
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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
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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
 
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  • #4
SteamKing
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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
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I think you mean when f = -ku

FWIW, sure, go ahead.

Yes, my bad. What is FWIW?

Thanks
 
  • #6
SteamKing
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FWIW = For What It's Worth
 
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  • #7
dextercioby
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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
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Thanks everyone.
 

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