Stability analysis of numerical methods for linear neutral Volterra delay-integro-differential system

This paper is concerned with the stability of numerical methods for linear neutral Volterra delay-integro-differential system. A sufficient condition such that the system is asymptotically stable is derived. Furthermore, it is proved that every linear θ-method with θ ∈ (1/2, 1] and A-stable BDF method preserve the delay-independent stability of its exact solutions. Finally, the numerical experiments are given to demonstrate the conclusions.