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Do different forms of Green's functions give same result?

  1. Apr 17, 2013 #1
    I'm solving Helmholtz equation in a cylindrical coordinate. With boundary conditions be Neumann type, I can write several satisfactory forms of the Green's function, right? (for example, I can make the discontinuity of the derivative of the Green's fucntion in the radial part, or in the z direction part.) Then I use them to get a solution for a specific problem with a source inside the cylinder, will they give the same solution?

    Apparently, they are written in different forms. When I study the properties of these solutions, I find that in one form, it will give divergence at some point, while the other one won't at the same point. That makes me very confused! Should they be the same, even though I'm using different forms of the Green's function? I thought they should at least be equivalent. If that's not the case, I don't understand why people can choose whatever form of the Green's function they like when they tackle the problem.

    FYI, the boundary condition is the derivative vanishes at the top, the bottom and also the inner surface of the cylinder.

    Really appreciate your help if you can clarify it:)
  2. jcsd
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