  The method of self-similar factor approximants is shown to be very convenient
for solving different evolution equations and boundary-value problems typical
of physical applications. The method is general and simple, being a
straightforward two-step procedure. First, the solution to an equation is
represented as an asymptotic series in powers of a variable. Second, the series
are summed by means of the self-similar factor approximants. The obtained
expressions provide highly accurate approximate solutions to the considered
equations. In some cases, it is even possible to reconstruct exact solutions
for the whole region of variables, starting from asymptotic series for small
variables. This can become possible even when the solution is a transcendental
function. The method is shown to be more simple and accurate than different
variants of perturbation theory with respect to small parameters, being
applicable even when these parameters are large. The generality and accuracy of
the method are illustrated by a number of evolution equations as well as
boundary value problems.
