u(0,t) = sin(2*PI*t), 0<t<1
= 0 , t>1
Boundary Conditions - Diff Eq
I have a problem with a question on my final exam. I do not expect nor want any help just a simple yes or no will suffice.
I am solving the classic wave equation using the Laplace Transform method extended to partial derivatives. Not a problem. The issue is I have never run across a boundary condition such as this:
(Note: there is no u(L,t) boundary condition specified. The usual initial conditions are specified)
I have seen limits, constants and functions for boundary conditions, but never a boundary condition such as this.
So on to my question... has anyone ever seen a boundary condition like this?
[smile] Check box: [ ] Yes [ ] No
(*) Sense this is a take home final I checked the book for any boundary value problems similar to this.
With "usual initial conditions" I assume you mean u(x,0) = f(x) and du(x,0)/dt = g(x) ?
If so, yes, the given boundary condition is a type of Dirichlet boundary condition (also known as boundary condition of first kind), defining u(0,t) = h(t)
So yes, I have seen them.
- M
If so, yes, the given boundary condition is a type of Dirichlet boundary condition (also known as boundary condition of first kind), defining u(0,t) = h(t)
So yes, I have seen them.
- M
Quote:Original post by thebolt00
With "usual initial conditions" I assume you mean u(x,0) = f(x) and du(x,0)/dt = g(x) ?
Yes, in this case, the initial displacement and velocity.
Quote:
If so, yes, the given boundary condition is a type of Dirichlet boundary condition (also known as boundary condition of first kind), defining u(0,t) = h(t)
So yes, I have seen them.
- M
Thanks
btw... It always helps to RTFT. There is a sentence stating:
Look for a solution which decays to zero with increasing X for all time.
(so... u(x,t) -> 0 as x -> infinity )
I hate it when I reach burn out during finals.
[Edited by - smc on May 13, 2007 11:25:53 AM]
Folks, no problems here in this case, but just want to remind everyone to be careful when replying to school related questions. Advice, hints are okay, but I don't want to see any answers!
This topic is closed to new replies.
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