Euler Method for a Class of Linear Impulsive Neutral Differential Equations

Abstract

This paper presents a new numerical scheme for a class of linear impulsive neutral differential equations with constant coefficients based on the Euler method. We rigorously establish the first-order convergence of the proposed numerical approach. Additionally, the asymptotical stability of the exact solutions and numerical solutions of impulsive neutral differential equations are studied. To substantiate our findings, two illustrative examples are provided, demonstrating the theoretical conclusions of this paper.

Keywords

• impulsive neutral differential equations
• convergence
• asymptotical stability
• Euler method