【摘要】 研究聚焦于一类非线性脉冲比例延迟微分方程的稳定性问题.首先，探讨了该方程解析解的稳定性与渐近稳定性；随后，进一步分析了该类方程数值解的稳定性，并采用Runge-Kutta方法求解刚性脉冲比例延迟微分方程，证明了该方法在代数稳定条件下保持该方程数值解稳定性和渐近稳定性；最后，通过数值试验，验证了理论结果的正确性.更多还原

【Abstract】 The research focuses on the stability issues of a class of nonlinear impulsive pantograph differential equations. The stability and asymptotic stability of their Analytical solutions were first investigated. Subsequently, the stability of numerical solutions for this class of equations was further analyzed. By employing the RungeKutta method to solve the stiff impulsive pantograph differential equations, it was proven that the method can maintain stability and asymptotic stability under algebraically stable conditions. Finally, the correctness of the theoretical results was verified through numerical experiments.更多还原