# Is Helmholtz equation a Poisson Equation?

1. Oct 16, 2013

### yungman

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

So is helmholtz equation a form of Poisson Equation?

2. Oct 16, 2013

### SteamKing

Staff Emeritus
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. Oct 16, 2013

### yungman

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: Oct 16, 2013
4. Oct 16, 2013

### SteamKing

Staff Emeritus
I think you mean when f = -ku

5. Oct 16, 2013

### yungman

Yes, my bad. What is FWIW?

Thanks

6. Oct 16, 2013

### SteamKing

Staff Emeritus
FWIW = For What It's Worth

7. Oct 16, 2013

### dextercioby

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. Oct 16, 2013

### yungman

Thanks everyone.