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Plotting the wave equation

  1. Nov 10, 2012 #1
    $$
    u(x,t) = \frac{1}{2}\int_{x - t}^{x + t}g(s)ds = \begin{cases}
    t, & (x,t)\in R_1\\
    \frac{1}{2}(1 - x + t), & (x,t)\in R_2\\
    \frac{1}{2}(x + t + 1), & (x,t)\in R_3\\
    1, & (x,t)\in R_4\\
    0, & (x,t)\in R_5,R_6
    \end{cases}
    $$
    where
    \begin{alignat*}{3}
    R_1 & = & \{(x,t):-1 < x - t < 1\text{ and } -1 < x + t < 1\}\\
    R_2 & = & \{(x,t):-1 < x - t < 1\text{ and } x + t > 1\}\\
    R_3 & = & \{(x,t):x - t < -1\text{ and } -1 < x + t < 1\}\\
    R_4 & = & \{(x,t):x - t < -1\text{ and } x + t > 1\}\\
    R_5 & = & \{(x,t):x + t < -1\}\\
    R_5 & = & \{(x,t):x - t > 1\}
    \end{alignat*}
    How do I plot this in the Mathematica?
    I tried this but it doesn't work.
    Code (Text):

    u[x_, t_] =
      Piecewise[{{t, -1 < x - t < 1 And - 1 < x + t <
          1}, {1/2 (1 - x + t), -1 < x - t < 1 And x + t >
          1}, {1/2 (x + t + 1), x - t < -1 And - 1 < x + t < 1}, {1,
         x - t < -1 And x + t > 1}, {0, x + t < -1}, {0, x - t > 1}}];
    Manipulate[Plot[u[x, t], {x, -10, 10}], {t, 0, 1, .01}]
     
     
  2. jcsd
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