Perturbation calculations beyond the first order result in the summations over the {\it complete spectrum} of unperturbed quantum system. The evaluation of perturbative expansions is a complex task, especially when the quantum system has a continuum part of the spectrum as it is the case for many quantum systems of practical interest like atoms and molecules. Therefore, the accurate methods which are able to treat the complete spectrum are highly desirable.

In this talk, we will present and discuss the {\it Green's function method} which provides an implicit summation over the complete spectrum and has been found accurate. The applications of Green's function method in \textit{atomic physics} will be outlined, and the numerical methods to evaluate a central-field Green's function in relativistic framework will be depicted carefully. Additionally, a {\it differential equation method} will be presented as an alternative to the Green's function method. Although the differential equation method is less general than Green's function method, it is more appropriate for {\it many-electron systems.}