A numerical method for a nonlocal hyperbolic model arising from a reliability system (Q1433094)

\textit{D. Shi} and \textit{W. Li} [Acta Math. Appl. Sin., Engl. Ser. 9, No. 1, 88--91 91993; Zbl 0783.60086)] developed a nonlocal hyperbolic model for the study of repairable systems (two-unit reliability system with shut-off rule) and showed that it can be reduced to a system of (Volterra-type) integral equations. The existence and uniqueness of its solution was analyzed by \textit{A. S. Ackleh}, \textit{K. Deng} and \textit{W. Li} [IMA J. Appl. Math. 68, No. 2, 135--148 (2003; Zbl 1046.35068)]. The present paper deals with the numerical solution of this system of integral equations. The proposed method consists in first constructing (by Gauss-Seidel-type iteration) a sequence of functions that converge monotonically to the solution, followed by the appropriate discretization of the equations defining the approximating functions. A number of examples (including one arising in a practical application) are used to illustrate the performance of the numerical scheme.