Simple PDE.... I'm trying to solve the PDE: [itex]\frac{\partial^2 f(x,t)}{\partial x^2}=\frac{\partial f(x,t)}{\partial t}[/itex] with [itex]x \in [-1,1][/itex] and boundary conditions f(1,t)=f(-1,t)=0. Thought that [itex]e^{i(kx-\omega t)}[/itex] would work, but that obviously does not fit with the boundary conditions. Has anyone an idea?
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.
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?
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).