A recurrence method for a special class of continuous time linear programming problems

This article studies a numerical solution method for a special class of continuous time linear programming problems denoted by (SP). We will present an efficient method for finding numerical solutions of (SP). The presented method is a discrete approximation algorithm, however, the main work of computing a numerical solution in our method is only to solve finite linear programming problems by using recurrence relations. By our constructive manner, we provide a computational procedure which would yield an error bound introduced by the numerical approximation. We also demonstrate that the searched approximate solutions weakly converge to an optimal solution. Some numerical examples are given to illustrate the provided procedure.