Is Helmholtz equation a Poisson Equation?

yungman · Oct 16, 2013

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

So is helmholtz equation a form of Poisson Equation?

SteamKing · Oct 16, 2013

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.

yungman · Oct 16, 2013

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

SteamKing · Oct 16, 2013

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.

yungman · Oct 16, 2013

SteamKing said: ↑

I think you mean when f = -ku

FWIW, sure, go ahead.

Yes, my bad. What is FWIW?

Thanks

SteamKing · Oct 16, 2013

FWIW = For What It's Worth

dextercioby · Oct 16, 2013

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.

yungman · Oct 16, 2013

Thanks everyone.

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Is Helmholtz equation a Poisson Equation?

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