laplace's equation - disc

leanne486

New member
Joined
Apr 25, 2006
Messages
1
What’s the best way to solve this problem?

Solve Laplace's Eqn.

(1/р)(∂u/∂Ф) + (1/р)(∂u/∂р) + (∂u/∂р) = 0

in the semidisc {( р , Ф ): 0<= р <1; -pi < Ф <pi}, w/ boundary conds.

U(1, Ф) = cos Ф.



So far I have

U(р , Ф)= A0 + Σ(n=1, ∞) (р^n)(An cos (n Ф) + Bn sin (n Ф))

Therefore:

U(1, Ф)= A0 + Σ(n=1, ∞) (An cos (n Ф) + Bn sin (n Ф)) Ξ cos Ф.

cos Ф = (3cos(Ф) + cos(3 Ф)) / 4.


I think I need to find the fourier coefficients next but am not sure how to. Thanks.
 

royhaas

Full Member
Joined
Dec 14, 2005
Messages
832
From the boundary condition and the trig identity, it appears that only 2 of the Fourier coefficients are not zero.
 
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