somewhere near the beginning.

I would appreciate it greatly …

Filed under: Mathematics — Alex @ 10:20 am 4/17/2007

if someone would solve this PDE analytically: u_{xx} \frac{4 (h^2 + a^2 x^2)}{(b+2 a y)^2} - u_{xy} \frac{4 a x}{b + 2 a y} + u_x \frac{8a^2 x}{(b+ 2 a y)^2} + u_{yy} = -h^2 on the unit square with u =0 on the right hand and bottom sides, and u_x = 0 on the right hand side,  u_y - \frac{2 a x}{b + 2a}u_x = 0 on the top side. Any takers?

We’re supposed to solve this numerically (at least, I believe this is the correct PDE– it was a poisson problem with mixed BCs in a nonstandard geometry, this is the result of a change of coordinates). The instructor gave a reference solution for a choice of the parameters, but my results don’t match; I’m going crazy debugging.

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