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

Abstract

This paper is devoted to examining the stability of Runge–Kutta methods for solving nonlinear delay-integro-differential-algebraic equations (DIDAEs). The stability of exact solution for nonlinear DIDAEs is obtained by using the Halanay’s inequality. 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.