On the One-Leg Methods for Solving Nonlinear Neutral Differential Equations with Variable Delay

Abstract

Based on A-stable one-leg methods and linear interpolations, we introduce four algorithms for solving neutral differential equations with variable delay. A natural question is which algorithm is better. To answer this question, we analyse the error behavior of the four algorithms and obtain their error bounds under a one-sided Lipschitz condition and some classical Lipschitz conditions. After extensively numerically experimenting, we give a positive conclusion.