# Simple PDE...

by Aidyan
Tags: simple
 P: 92 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?
Emeritus
PF Gold
P: 9,772
 Quote by Aidyan 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?
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.
P: 92
 Quote by Hootenanny 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.
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?

Emeritus