Approximate solution of initial-value problem for retarded differential equations on complex domain

In 1980–1984, V. K. Dzyadyk suggested and modified an iterative approximation method (IA-method) for a numerical solution of the Cauchy problem: y′ = f(x,y), y(x0) = y0 (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 equations on complex domain. At, the end, the method was tested numerically by four different examples.