HWK 3, Due Tue Apr 11
Make your write-up clean and concise. I do not need to see all you algebra. Imagine that you are writing an example for a book. The main steps have to come out clearly but all the details should not be shown.

Consider Poisson's equation with forcing (R2 -r2 ) cos a in the cylinder of radius R with boundary condition u(R,a)=0 , where r, a represent the distance from the origin and the azimuthal angle, respectively.

  1. Solve the problem using an appropriate series expansion.
  2. Solve the problem numerically using a finite difference or finite element approximation. Your approximation should be 2nd order accurate.
  3. Plot both results on the same figure. Comment briefly on the numerical effectiveness of both approaches.