sin = ClearAll
a = 50
T = 60000
L = \[Pi]
NDSolve[{I*\!\(
\*SubscriptBox[\(\[PartialD]\), \(t\)]\(y[x, t]\)\) + .0004*\!\(
\*SubscriptBox[\(\[PartialD]\), \(x, x\)]\(y[x, t]\)\) == 0,
y[-a, t] == y[a, t],
y[x, 0] ==
Piecewise[{{0, x < -L/2}, {0,
x > L/2}, {Sqrt[2/L] Cos[x], -L/2 <= x <= L/2}}]}, y, {x, -a,
a}, {t, 0, T}]
Plot3D[Evaluate[Abs[y[x, t]] /. %], {x, -a, a}, {t, 0, T},
PlotRange -> All, PlotPoints -> 200, MaxRecursion -> 2]
Sorry about that.
