Simple PDE...

  1. 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?
     
  2. jcsd
  3. Hootenanny

    Hootenanny 9,681
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    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.
     
  4. Re: Simple PDE....

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

    Hootenanny 9,681
    Staff Emeritus
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    Gold Member

    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).
     
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