The publication is devoted to the analysis of the Harrod-Domar nonlinear model of economic growth, based on the model of sensitivity to initial conditions. This model is based on assumptions on the nonlinearity of the production function and periodic character of the volume of consumption. Instead of the traditional solution of the Cauchy problem and the definition of economic growth as the end of the transition process it is proposed to seek T-periodic solution. Equation of the model with initial conditions at the edges of the period has the form of two-point boundary value problem. Numerical integration of differential equation in the interval of time equal to the period T and the found solution for t=T is specified by the iterative formula of Newton. The condition for determining periodic solutions is equal to zero objective function.