On the solutions of a system of linear retarded and advanced differential equations by the Bessel collocation approximation

In this study, we present a numerical approximation for the solutions of the system of high-order linear retarded and advanced differential equations with variable coefficients under the mixed conditions. This method is based on taking the truncated Bessel expansion of the functions in the retarded and advanced differential equation system. By the aid of the matrix operations and the collocation points, the problem is transformed into a matrix equation with the unknown Bessel coefficients. By solving this matrix equation, the unknown coefficients of the approximate solutions are computed. In addition, examples that illustrate the pertinent features of the method are presented, and the results of this investigation are discussed.