  We demonstrate via several examples how the backward error viewpoint can be
used in the analysis of solutions obtained by perturbation methods. We show
that this viewpoint is quite general and offers several important advantages.
Perhaps the most important is that backward error analysis can be used to
demonstrate the validity of the solution, however obtained and by whichever
method. This includes a nontrivial safeguard against slips, blunders, or bugs
in the original computation. We also demonstrate its utility in deciding when
to truncate an asymptotic series, improving on the well-known rule of thumb
indicating truncation just prior to the smallest term. We also give an example
of elimination of spurious secular terms even when genuine secularity is
present in the equation. We give short expositions of several well-known
perturbation methods together with computer implementations (as scripts that
can be modified). We also give a generic backward error based method that is
equivalent to iteration (but we believe useful as an organizational viewpoint)
for regular perturbation.
