# Simple PDE

1. Oct 17, 2011

### Aidyan

Simple PDE....

I'm trying to solve the PDE:

$\frac{\partial^2 f(x,t)}{\partial x^2}=\frac{\partial f(x,t)}{\partial t}$ with $x \in [-1,1]$ and boundary conditions f(1,t)=f(-1,t)=0.

Thought that $e^{i(kx-\omega t)}$ would work, but that obviously does not fit with the boundary conditions. Has anyone an idea?

2. Oct 17, 2011

### Hootenanny

Staff Emeritus
Re: Simple PDE....

Your equation is the 1D heat equation, the solutions of which are very well known and understood. A google search should yield what you need.

P.S. You will also need some kind of initial condition.

3. Oct 17, 2011

### Aidyan

Re: Simple PDE....

Hmm... looks like it isn't just a simple solution, however. It seems I'm lacking the basics ... I thought this is sufficeint data to solve it uniquely, what is the difference between boundary and initial conditions?

4. Oct 17, 2011

### Hootenanny

Staff Emeritus
Re: Simple PDE....

Afraid not, without knowing the temperature distribution at a specific time you aren't going to obtain a (non-trivial) unique solution.
The former specifies the temperature on the spatial boundaries of the domain (in this case x=-1 and x=1). The latter specifies the temperature distribution at a specific point in time (usually t=0, hence the term initial condition).