Approximate solutions of nonlinear integro-differential equations on complex domain

In 1980–1984, V. K. Dzaydyk suggested and modified an iterative approximation method (IA-method) for 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. Dzaydyk to study the approximation of the solution for the nonlinear Integro-differential equations on complex domain. At the end, the method was tested numerically by four different examples.