  We study numerically the fully nonlinear spherically-symmetric collapse of a
self-gravitating, minimally-coupled, massless scalar field. Our numerical code
is based on double-null coordinates and on free evolution of the metric
functions and the scalar field. The numerical code is stable and second-order
accurate. We use this code to study the late-time asymptotic behavior at fixed
$r$ (outside the black hole), along the event horizon, and along future null
infinity. In all three asymptotic regions we find that, after the decay of the
quasi-normal modes, the perturbations are dominated by inverse power-law tails.
The corresponding power indices agree with the integer values predicted by
linearized theory. We also study the case of a charged black hole nonlinearly
perturbed by a (neutral) self-gravitating scalar field, and find the same type
of behavior---i.e., quasi-normal modes followed by inverse power-law tails,
with the same indices as in the uncharged case.
