- #1
tjackson3
- 150
- 0
Homework Statement
Consider
[tex]\frac{\partial u}{\partial t} = k\frac{\partial^2u}{\partial x^2}[/tex] subject to
[tex]u(0,t) = A(t),\ u(L,t) = 0,\ u(x,0) = g(x).[/tex] Assume that u(x,t) has a Fourier sine series. Determine a differential equation for the Fourier coefficients (assume appropriate continuity).
Homework Equations
Coefficients of the Fourier sine series of [itex]f(x)[/itex]:
[tex]B_n = \frac{2}{L}\int_0^L f(x)\sin(n\pi x/L)\ dx[/tex]
The Attempt at a Solution
I'm stuck just getting a start. The problem is that [itex]u(x,t)[/itex] will not converge to its Fourier sine series at x = 0 unless A(t) is identically zero. This also kills the ability to perform term-by-term differentiation on the FSS. It seems impossible to impose the boundary condition at x = 0. Thoughts?
Last edited by a moderator: