Nonlinear stability of one-leg methods for neutral Volterra delay-integro-differential equations

This paper concerns the numerical stability of one-leg methods for nonlinear neutral Volterra delay-integro-differential equations with constant delay. G(c, p)-algebraically stable one-leg methods with compound quadrature formulae are considered. Nonlinear stability conditions for the presented methods are derived. As an illustration of the application of these investigations, the stability results of one-leg methods for Volterra delay-integro-differential equations are obtained, which are more general than the related results in the previous literature. Two numerical experiments are given to confirm our results.