APPROXIMATE SOLUTION OF INITIAL-VALUE PROBLEM, FOR RETARDED DIFFERENTIAL-EQUATIONS ON COMPLEX-DOMAIN

In 1980-1984, V. K. Dzyadyk suggested and modified an iterative approx imation method (IA-method) for a numerical solution of the Cauchy prob lem: y' = f(x, y), y(x(0)) = y(0) (see [1-3]). In this paper, we will use the same technique of V. K. Dzyadyk to study the approximation of the solution for the initial-value problem for retarded differential e quations on complex domain. At, the end, the method was tested numeric ally by four different examples.