Characteristic roots of a second order retarded functional differential equation via spectral-tau method

Abstract

In this paper, we have found the solution of second-order delay differential equations of retarded type with multiple delays. As well as developing an approximation for finding characteristic roots for such delay differential equations via the method of spectral tau which depends on the basis mixed Fourier basis or shifted Chebyshev polynomials.

Analytical Solutions for Advanced Functional Differential Equations with Discontinuous Forcing Terms and Studying Their Dynamical Properties

“…Recently, Abdullah and et al found analytical solutions of retarded dynamical systems of the third order and of the n th order by using Lambert W function and a discussion of their stability in their two papers (7)(8) respectively. Abdullah and et al found approximate characteristic roots for DDEs with multiple delays via the method of spectral tau (9).…”