Stability analysis of block boundary value methods for the neutral differential equation with many delays

This paper mainly deals with the asymptotic stability properties of block boundary value methods (B2VMs) for the neutral differential equation with many delays. For the time lagging arguments, a technique of Lagrange interpolation is considered. Under some certain conditions, it is proved that B2VMs can preserve the asymptotic stability of exact solutions for the neutral differential equation with many delays if and only if B2VMs are A-stable for ordinary differential equation. Moreover, some numerical experiments are given to confirm the main conclusion.