On the numerical solution of second order delay differential equations via a novel approach

Delay differential equations belong to an important class of differential equations in which the evolution of the state depends on the previous time.This work proposes a novel approach for the numerical solution of delay differential equations of second order.The suggested numerical scheme is based on Laplace transform (LT) technique.In the suggested technique, first, the given equation is transformed using the LT method to an algebraic expression.The expression is then solved for the unknown transformed function and finally the well-known Weeks method is utilized to convert the solution back to time domain.Functional analysis was used to examine the existence and uniqueness of the considered equations and to generate sufficient requirements for Ulam-Hyers (UH) type stability.Furthermore, we consider different numerical example from literature to validate our method.