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Green functions

  1. Jun 8, 2006 #1
    I need a list of Green functions,
    for different types of equations and dimensions.

    I have tried to use google but with no success.
     
  2. jcsd
  3. Jun 8, 2006 #2

    rcgldr

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    Homework Helper

    I got a bunch of hits with a google for "green's theorem", but I'm not sure if there are other functions you're looking for.
     
  4. Jun 8, 2006 #3

    FredGarvin

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    Science Advisor

    Green functions are not the same thing as Green's Theorem.

    I can't honestly say that I have seen anything tabulated. I can't say that I have ever looked for anything like that though either. I was always under the impression that green fuctions are dependent on boundary conditions and the Diff. Eq's being used. I'll keep my eyes open to see if I find anything. You might try searching with "Green's functions" as well. I have heard them refered to in both ways.

    EDIT: The first hit I got using the "green's function" search...
    http://mathworld.wolfram.com/GreensFunction.html
     
  5. Jun 8, 2006 #4
    Thx. Yes they are dependent on boundary conditions. But for the more simple cases i was sure to find tables of green functions.

    Something like

    [tex]-\frac {1} {2\pi}ln(\rho_1- \rho_2) ;\frac {i} {4}H_0[k(\rho_1- \rho_2)];\frac {1} {2\pi}K_0[k(\rho_1- \rho_2)][/tex]

    for Laplace, Helmholtz and modified Helmholtz in the plane when G goes to 0 as r goes to infinity.
    And also in 3 dimensions, for a sphere with homegenous diricihlet on the boundary, the diffusion equation, the wave equation etc.

    Green functions are very useful when solving P.D.E and therefor i thought i could find some good tables. But none of my mathematical handbooks have this and i havent found any on internet yet either.
     
    Last edited: Jun 8, 2006
  6. Jun 8, 2006 #5
    There exists no such list since a "Green Function" is any function whose Laplacian equals [itex]\delta[/itex](|x-x'|). There is an infinity of such functions.

    Pete
     
  7. Jun 8, 2006 #6
    Green functions are not confined to differential equations containing the Laplacian, they work under an arbitrary differential operator. The Green function is by definition the solution to a differential equation under application of a unit impulse source term. The beautiful thing about Green functions is that once I know the solution for a unit impulse, I can obtain the solution for an arbitrary source by a convolution of the Green function with that source. This is of course predicated on linearity of the solutions.
     
  8. Jun 8, 2006 #7
    Check out the first chapter or two of Jackson Electrodynamics for everything you would ever care to know about green functions.
     
  9. Jun 10, 2006 #8
    Thats the Green function for the Laplace operator.
    How is a general green function different from general solutions to ODEs, integrals etc? There are tables of those.
    I found a short table of green functions in Arfken.
     
  10. Jun 10, 2006 #9
    Thx, but thats probably Laplace and Poisson differential operator only?
     
  11. Jun 10, 2006 #10
  12. Jun 16, 2006 #11
    Thanks for your answer!
     
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