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

A computational approximation for the solution of retarded functional differential equations and their applications to science and engineering