# Is Helmholtz equation a Poisson Equation?

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
Staff Emeritus
Homework Helper
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.

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:
SteamKing
Staff Emeritus
Homework Helper
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

I think you mean when f = -ku

Yes, my bad. What is FWIW?

Thanks

SteamKing
Staff Emeritus
Homework Helper
FWIW = For What It's Worth

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