  We present high resolution spherically symmetric relativistic
magnetohydrodynamical simulations of the evolution of a pulsar wind nebula
inside the free expanding ejecta of the supernova progenitor. The evolution is
followed starting from a few years after the supernova explosion and up to an
age of the remnant of 1500 years. We consider different values of the pulsar
wind magnetization parameter and also different braking indices for the
spin-down process. We compare the numerical results with those derived through
an approximate semi-analytical approach that allows us to trace the time
evolution of the positions of both the pulsar wind termination shock and the
contact discontinuity between the nebula and the supernova ejecta. We also
discuss, whenever a comparison is possible, to what extent our numerical
results agree with former self-similar models, and how these models could be
adapted to take into account the temporal evolution of the system. The inferred
magnetization of the pulsar wind could be an order of magnitude lower than that
derived from time independent analytic models.
