We study a numerical method for solving a system of Volterra-renewal integral equations with space fluxes,that represents the Chapman-Kolmogorov equation for a class of piecewise deterministic stochastic processes.The solution of this equation is related to the time dependent distribution function of the stochastic process and it is a non-negative and non-decreasing function of the space.Based on the Bestein polynomials,we build up and prove a non-negative and non-decreasing numerical method to solve that equation,with quadratic convergence order in space.