  In this lectures various methods which give a possibility to extend an area
of applicability of perturbation series and hence to omit their local character
are analysed. While applying asymptotic methods as a rule the following
situation appears: the existence of asymptotics for $\ve\rightarrow 0$ implies
an existence of the asymptotics for $\ve\rightarrow\infty$. Therefore, the idea
to construct one function valid for the whole parameter interval for $\ve$ is
very attractive. The construction of asymptotically equivalent functions
possessing a known asymptotic behaviour for $\ve\rightarrow 0$ and
$\ve\rightarrow \infty$ will be discussed. Using summation and interpolation
procedures we focus on continuous models derived from a discrete
micro-structure. Various continualization procedures that take the non-local
interaction between variables of the discrete media into account are analysed.
