  Delay differential equations are of great importance in science, engineering,
medicine and biological models. These type of models include time delay
phenomena which is helpful for characterising the real-world applications in
machine learning, mechanics, economics, electrodynamics and so on. Besides,
special classes of functional differential equations have been investigated in
many researches. In this study, a numerical investigation of retarded type of
these models together with initial conditions are introduced. The technique is
based on a polynomial approach along with collocation points which maintains an
approximated solutions to the problem. Besides, an error analysis of the
approximate solutions is given. Accuracy of the method is shown by the results.
Consequently, illustrative examples are considered and detailed analysis of the
problem is acquired. Consequently, the future outlook is discussed in
conclusion.
