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Separation of variables

  1. Dec 19, 2009 #1
    When solving a pde using this method how do you know what ORDER to use the initial/boundary conditions given to you?

    E.g. if you are asked to solve the wave equation given u(x,0), u'(x,0), u(0,t), u(l,t) how do you know what order to use these in (particularly the first two)
     
  2. jcsd
  3. Dec 19, 2009 #2
    Re: Seperation of variables

    You need to solve the boundary value problem first, so that you can write the solution to the temporal equation in terms of the eigenvalues of the boundary value problem.
     
  4. Dec 20, 2009 #3
    Re: Seperation of variables

    Thanks, but after you use the two boundary conditions how do you know what order to use the two initial conditions
     
  5. Dec 20, 2009 #4
    As far as situations I've seen, it doesn't matter what order you use them in. In the wave equation example you gave, the initial conditions will independently determine the constants.
     
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