- #1
selzer9
- 2
- 0
I'm not sure how to solve this:
du/dt = 3 [itex]\frac{d^{2}u}{dx^{2}}[/itex]
These are the conditions:
u(0,t)= -1
u(pi,t)= 1
u(x,0) = -cos 7x
Suggestion:
I should use steady state solution to get a homogeneous initial condition.
Starting with separtion of variables
u(x,t) = G(x)H(t)
And du/dt = GH' and d^2u/dx^2 = G"H
So GH'= c^2 G"H
and H'/(c^2)H = G"/G
Then H'/(c^2)H = k = G"/G
thus H' - (c^2)Hk = 0 and G" - Gk = 0.
Once here how do I make sure u(x,t) follows the conditions?
du/dt = 3 [itex]\frac{d^{2}u}{dx^{2}}[/itex]
These are the conditions:
u(0,t)= -1
u(pi,t)= 1
u(x,0) = -cos 7x
Suggestion:
I should use steady state solution to get a homogeneous initial condition.
Starting with separtion of variables
u(x,t) = G(x)H(t)
And du/dt = GH' and d^2u/dx^2 = G"H
So GH'= c^2 G"H
and H'/(c^2)H = G"/G
Then H'/(c^2)H = k = G"/G
thus H' - (c^2)Hk = 0 and G" - Gk = 0.
Once here how do I make sure u(x,t) follows the conditions?