Various sorts of asymptotic-numerical methods have been proposed in th
e literature: the reduced basis technique, direct computation of serie
s or the use of Pade approximants. The efficiency of the method may al
so depend on the chosen path parameter, on the order of truncature and
on alternative parameters. In this paper, we compare the three classe
s of asymptotic- numerical method, with a view to define the ''best''
numerical strategy.