Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Simple PDE

  1. Oct 17, 2011 #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. Oct 17, 2011 #2

    Hootenanny

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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. Oct 17, 2011 #3
    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. Oct 17, 2011 #4

    Hootenanny

    User Avatar
    Staff Emeritus
    Science Advisor
    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).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Simple PDE
  1. Simple PDE (Replies: 3)

  2. Simple PDE (Replies: 2)

  3. Simple PDE Question (Replies: 4)

  4. A very simple PDE (Replies: 2)

Loading...