Accuracy of the Laplace transform method for linear neutral delay differential equations

Abstract

In this paper, we study and solve linear neutral delay differential equations. We investigate the reliability and accuracy of applying the Laplace transform to obtain the solutions of linear neutral delay differential equations. These types of equations are more difficult to solve because the time delay appears in the derivative of the state variable. We rely on computer algebra and numerical methods to determine the poles which are required for computing the inverse Laplace transform. The form of the resulting solution is a non-harmonic Fourier series. A sufficient degree of accuracy can often be achieved by using a relatively small number of terms in the associated truncated series. We compare these solutions with the solutions obtained by the classical method of steps and numerical solutions obtained by the discretization of the linear delay differential equations. It is shown that the Laplace transform method provides very reliable and accurate solutions.