This article deals with a class of numerical methods for retarded diffierential algebraic systems with time-variable delay.The methods can be viewed as a combination of Runge-Kutta methods and Lagrange interpolation.A new convergence concept,called DA-convergence,is introduced.The DA-convergence result for the methods is derived.At the end,a numerical example is given to verify the computational effiectiveness and the theoretical result.
A type of complex systems under both random influence and memory effects is considered. The systems are modeled by a class of nonlinear stochastic delay-integrodifferential equations. A delay-dependent stability criterion for such equations is derived under the condition that the time lags are small enough. Numerical simulations are presented to illustrate the theoretical result.
