I am working through a PDE and get through to the general solution, but get a seemingly zero Fourier coefficient.
Using seperable variables method and setting the general solution and substituting into original equation:
where is an arbitary constant. Solving the ODE's given yields:
->now apply second condition
since always satisfies the zero condition
rewrite infinite solution as a fourier series.
I evaluated the terms to simplify first:
now back into integral:
It is this last part I always seem to have the expression collapsing to zero; since and are always the same with the limits of
I know I must have made a mistake somewhere, I suspect in changing the period length and associated limits ,but can't see it!
Many thanks for reading.