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Laplace solution in polar coordinates

  1. Feb 8, 2010 #1
    Hello, its been a pleasure finding you:smile:

    I have an asignment due to the end of this week and due to some problems, i hadn't found time to get to it so far.

    I have to calculate the exact solution of the Laplace equation in polar coordinates, in a hollow disk in the domain Ω

    where R1<=r<=R2 and 0<=θ<=2π

    and with the following boundary conditions

    φ(R1,θ)=0 and φ(R2,θ)=sin2θ

    I would be in debt to anyone who can assist me or refer me to a link that can be helpful

    [edit] unfortunately i didn't see soon enough the 2nd sticky :( please move my post to the right thread..I'm sorry for the inconvinience..
    Last edited: Feb 8, 2010
  2. jcsd
  3. Feb 8, 2010 #2


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    What is Laplace's equation in polar coordinates? You should be able to separate it into equation for the [itex]\theta[/itex] and r dependencies separately.
  4. Feb 8, 2010 #3
    Its form would be the following:

    [tex]\frac{\partial^2f}{\partial r^2}+\frac{1}{r^2} \frac{\partial ^2f}{\partial \theta^2} + \frac{1}{ r} \frac{\partial f}{\partial r}= 0[/tex]

    From this stage, can you tell me how do I proceed?

    [edit] Suppose the solution i'm seeking is in the following form

    [tex]f(r,\theta) =C_0lnr + D_0 + \sum_{0}^\infty(C_nr+\frac{D_n}{r^n}).(A_ncosn\theta + B_nsinn\theta)[/tex]

    how do i find the constants that occur by my B.C? I know my questions are a bit amateur style but I'm quite confused
    Last edited: Feb 8, 2010
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