  One of the major challenges of contemporary mathematics is numerical solving
of various problems for functional differential equations (FDE), in particular
Cauchy problem for delayed and neutral differential equations. Recently large
variety of methods to handle this task appeared. In the paper, we present new
semi-analytical approach for FDE's consisting in combination of the method of
steps and a technique called differential transformation method (DTM). This
approach reduces the original Cauchy problem for delayed or neutral
differential equation to Cauchy problem for ordinary differential equation for
which DTM is convenient and efficient method. Moreover, there is no need of any
symbolic calculations or initial approximation guesstimates in contrast to
methods like homotopy analysis method, homotopy perturbation method,
variational iteration method or Adomian decomposition method. The efficiency of
the proposed method is shown on certain classes of FDE's with multiple constant
delays including FDE of neutral type. We also compare it to the current
approach of using DTM and the Adomian decomposition method where Cauchy problem
is not well posed.
