- #1
Jamin2112
- 986
- 12
Homework Statement
Solve the heat equation
ut=uxx
on the interval 0 < x < 1 with no-flux boundary conditions. Use the initial condition
u(x,0)=cos ∏x
Homework Equations
We eventually get u(x,t)= B0 + ƩBncos(n∏x/L)exp(-n2∏2σ2t/L2)
where
L=1 and σ=1 in our case.
B0 is given by (1/L)∫[0,L]u(x,0)dx
and Bn by (2/L)∫[0,L]u(x,0)cos(n∏x/L)dx
The Attempt at a Solution
Well, I keep getting Bn = (2/L)∫[0,L]u(x,0)cos(n∏x)dx = 0 after using the trig identity cos(u)cos(v)=(1/2)(cos(u+v)+cos(u-v)).
What's happening here? I've checked my steps many times.