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One of the major challenges of contemporary mathematics is numerical solvingof various problems for functional differential equations (FDE), in particularCauchy problem for delayed and neutral differential equations. Recently largevariety of methods to handle this task appeared. In the paper, we present newsemi-analytical approach for FDE's consisting in combination of the method ofsteps and a technique called differential transformation method (DTM). Thisapproach reduces the original Cauchy problem for delayed or neutraldifferential equation to Cauchy problem for ordinary differential equation forwhich DTM is convenient and efficient method. Moreover, there is no need of anysymbolic calculations or initial approximation guesstimates in contrast tomethods like homotopy analysis method, homotopy perturbation method,variational iteration method or Adomian decomposition method. The efficiency ofthe proposed method is shown on certain classes of FDE's with multiple constantdelays including FDE of neutral type. We also compare it to the currentapproach of using DTM and the Adomian decomposition method where Cauchy problemis not well posed.

A new semi-analytical approach for numerical solving of Cauchy problem for functional differential equations