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

Abstract EN

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.