Numerical stability of θ-methods of the functional multi-delay differential equations with piecewise continuous arguments

For the functional multi-delay differential equations with piecewise continuous arguments (EPCA), the theoretical stability condition which is independent on τ, τ∈(0,+∞) is defined. By applying the linear θ-method and the one-leg θ-method to the functional EPCA with the multi-delay, the order of convergence and the necessary and sufficient conditions under which the numerical methods replicate the stability behavior of the functional EPCA itself are provided.