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# Maple watch

1. Suppose (t,x) -> w(t, x) solves the following initial value problem:
w_tt(t, x)- w_xx(t, x) = 0 subject to

w(0,x) = phi(x)
w_t(0, x) = 0
where the function phi: R -> R is specied thus: Defne the function sigma : R- > R by

x
exp(-1=x) if x > 0
0 if x <= 0
(Note that sigma is defned piecewise). The function phi : R -> R is defned by
x -> sigma(x)sigma(1 -x)
and is plotted.

Use Maple to plot the solution w to the IVP in the w - x plane at each of the following time
steps: t = 0,2, 4, 6 in a single diagram.

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Updated: March 17, 2011
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