- #1
middleramen
Homework Statement
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)
Homework Equations
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.