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Laplace Equation Polar Form

  1. Apr 20, 2013 #1
    1. The problem statement, all variables and given/known data

    Solve the BVP:

    r[itex]^{2}[/itex]u[itex]_{rr}[/itex] + ru[itex]_{r}[/itex] + u[itex]_{ψψ}[/itex] = 0

    0 ≤ r ≤ 1, 0 < ψ < 2π

    u(1,ψ) = 0.5(π - ψ)



    2. Relevant equations



    3. The attempt at a solution

    I've derived the general solution of u(r,ψ) = C + r[itex]^{n}[/itex]Ʃ[itex]_{n}[/itex]a[itex]_{n}[/itex]cos nψ + b[itex]_{n}[/itex]sin nψ, where a,b, C are constants.

    Attempts to determine fourier constants don't give meaningful results.

    Also, it was my understanding that the boundary condition must be periodic, i.e. u(1,0) = u(1,2π), which is untrue for this problem.
     
  2. jcsd
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