About numerical methods for timed and continuous Petri nets

This article points out the influence of the time increment in numerical algorithms that concern Petri nets models. Shorts algorithms are proposed for T-timed Petri nets and continuous Petri nets with variable speeds to provide the marking evolution. Numerical errors are discussed in both cases. Concerning T-timed Petri nets, conditions are given such that numerical errors do not arise. Concerning continuous Petri nets with variable speeds the numerical errors are related to the solver and to the time increment. An example is proposed to point out the importance of the time increment choice.