  Understanding the evolution of a supernova remnant shell in time is
fundamental. Such understanding is critical to build reliable models of the
dynamics of the supernova remnant shell interaction with any pulsar wind nebula
it might contain. Here, we perform a large study of the parameter space for the
one-dimensional spherically symmetric evolution of a supernova remnant,
accompanying it by analytical analysis. Assuming, as is usual, an ejecta
density profile with a power-law core and an envelope, and a uniform ambient
medium, we provide a set of highly-accurate approximations for the evolution of
the main structural features of supernova remnants, such as the reverse and
forward shocks and the contact discontinuity. We compare our results with
previously adopted approximations, showing that existing simplified
prescriptions can easily lead to large errors. In particular, in the context of
pulsar wind nebulae modelling, an accurate description for the supernova
remnant reverse shock is required. We also study in depth the self-similar
solutions for the initial phase of evolution, when the reverse shock propagates
through the envelope of the ejecta. Since these self-similar solutions are
exact, but not fully analytical, we here provide highly-accurate approximations
as well.
