Approximation of the solutions of exponentially stable difference-differential equations

The algorithm of approximation of the domain of asymptotic stability of stationary system of difference-differential equations is developed. This approximation is based on the construction of the domain of asymptotic stability of corresponding difference schemes. The method is based on Adams scheme approximation of the solutions of difference-differential system with a delay. This system allows for exponentially stable linear approximation represented by the system of difference equations. The example illustrating feasibility of this approach is presented.