标题： Runge-Kutta 方法对非线性延迟积分微分代数方程的稳定性分析 显示英文标题

标题： Stability analysis of Runge-Kutta methods for nonlinear delay-integro-differential-algebraic equations

摘要： 本文致力于研究求解具有常数时滞的非线性Volterra延迟积分微分代数方程（DIDAEs）的Runge-Kutta方法的稳定性。分析了结合Runge-Kutta方法和复合求积规则的混合数值格式用于非线性DIDAEs。建立了保证所提出格式全局与渐近稳定的判据，并通过若干数值例子验证了理论结果。 显示英文摘要

摘要： This paper is devoted to examining the stability of Runge-Kutta methods for solving nonlinear Volterra delay-integro-differential-algebraic equations (DIDAEs) with constant delay. Hybrid numerical schemes combining Runge-Kutta methods and compound quadrature rules are analyzed for nonlinear DIDAEs. Criteria for ensuring the global and asymptotic stability of the proposed schemes are established. Several numerical examples are provided to validate the theoretical findings.