  Recent observations of Type Ia supernovae provide evidence for the
acceleration of our universe, which leads to the possibility that the universe
is entering an inflationary epoch. We simulate it under a ``big bounce'' model,
which contains a time variable cosmological ``constant'' that is derived from a
higher dimension and manifests itself in 4D spacetime as dark energy. By
properly choosing the two arbitrary functions contained in the model, we obtain
a simple exact solution in which the evolution of the universe is divided into
several stages. Before the big bounce, the universe contracts from a $\Lambda
$-dominated vacuum, and after the bounce, the universe expands. In the early
time after the bounce, the expansion of the universe is decelerating. In the
late time after the bounce, dark energy (i.e., the variable cosmological
``constant'') overtakes dark matter and baryons, and the expansion enters an
accelerating stage. When time tends to infinity, the contribution of dark
energy tends to two third of the total energy density of the universe,
qualitatively in agreement with observations.
