Delay differential equations, stability inequalities and numeric solutions

In this study, giving the classification of differential equations with delayed argument, will be analyzed delay differential equations with constant delay, delay differential equations with variable delay, neutral equations, equations with advanced argument and singularly perturbed delay boundary-value problem. Then Laplace transformations will be applied to solve differential equations with constant coefficients and delay arguments. Numerical solutions of a singularly perturbed linear boundary-value problem are discussed. Finally, stability inequalities for an integro-differential equation with delay will be presented. Further numerical results will be provided to assist the theoretical estimates.