Dirichlet Boundary Value on Disk Problem

G

Guest

Guest
Hi Everyone:

I am having problems with a Dirichlet boundary value for a disk question. They questions gives the conditions of:

0 <= r < 2, -pi <= theta <= pi
u(2,theta) = f(theta), -pi <= theta <= pi

The problem is to solve given f(theta) = cos^2 (x) (cosine squared of x)

This is in the "Fundamentals of Differential Equations" textbook p. 649 (section 10.7) problem # 8.

I was thinking I should use: u(r,theta) = a0/2 + SUM(an cos(n*theta) + bn sin(n*theta) and solve for an and bn.

I tried this for #7 (which has the answer in the back) but I didn't come close to the answer.

Anyone have any ideas?

Thanks!
 

royhaas

Full Member
Joined
Dec 14, 2005
Messages
832
If the coefficients of the sine terms are not identically zero, check your integration since you are approximating an even function. i.e., \(\displaystyle cos^2(x) = 0.5(1+cos(2x))\).
 
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