Next: 7.37, §6 Total Up: 7.37 Previous: 7.37, §4 Eigenfunctions

7.37, §5 Solve

Expand all variables in the problem for u in a Fourier series:

Put into P.D.E. uxx + uyy = 0:

Because of the choice of the Xn:

Put into B.C. uy(x,0) = p(x):

Put into B.C. uy(x,1) = q(x):

Solve this O.D.E. and boundary conditions for Cn:

For :

O.D.E.:

Boundary conditions give for An and Bn:

Solve for An and Bn using Gaussian elimination and clean up:

For n = 0:

O.D.E.:

C0 = A0 + B0 y

B.C.s:

Oops! This only works if

Also, A0 remains unknown!

No problem! Students will explain and fix.


Next: 7.37, §6 Total Up: 7.37 Previous: 7.37, §4 Eigenfunctions
11/27/00 0:42:24