Dirichlet Boundary Value on Disk Problem

[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]

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