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Is Helmholtz equation a Poisson Equation?

  1. Oct 16, 2013 #1
    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. jcsd
  3. Oct 16, 2013 #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.
     
  4. Oct 16, 2013 #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: Oct 16, 2013
  5. Oct 16, 2013 #4

    SteamKing

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    I think you mean when f = -ku

    FWIW, sure, go ahead.
     
  6. Oct 16, 2013 #5
    Yes, my bad. What is FWIW?

    Thanks
     
  7. Oct 16, 2013 #6

    SteamKing

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    FWIW = For What It's Worth
     
  8. Oct 16, 2013 #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.
     
  9. Oct 16, 2013 #8
    Thanks everyone.
     
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