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Solving the Wave Equation in semi-infinite domain with easy ICs

  1. Mar 25, 2013 #1
    Hi, so the problem is this:

    I am trying to solve (analytically) the wave equation with c=1:


    on x,t>0 given the initial conditions

    [tex]u(x,0)=u_{t}(x,0)=0, u(0,t)=sin(wt)[/tex]

    I know how to solve on semi-infinite domains for quite a few cases using Green's Functions, Fourier Transforms, D'Alembert's solution and separation of variables. But I keep getting u=0 with these familiar methods due to the initial conditions of u being 0 and unmoving at t=0.

    I feel like this is easier than I'm making it! Anyway, any help would be appreciated!
    Last edited: Mar 25, 2013
  2. jcsd
  3. Mar 25, 2013 #2
    Yeh... After solving numerically I realised that I just hadn't thought about the fact that the waves must propagate at speed 1 and u=0 for all x>t. So a quick bit of algebra gives:


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