movable singular point, nonlinear differential equation of the second order, approximate solution, neighborhood of the movable singular point, the complex region, posteriori error estimate.

In the rapidly developing modern world occupy a special place differential equations, which are mathematical models of many processes and phenomena occurring in various spheres of human activity. Research in the physical, economic and social areas are often faced with the necessity of solving differential equations, which requires the development of the theory of differential equations. But if the theory of linear differential equations corresponds to more demands placed upon it, the nonlinear differential equations are studied not enough. A significant obstacle is the presence of movable singular points, which nonlinear differential equations relate to the category in general is not solvable in quadratures [1]. In the paper we use the method of solving the above equations, which proposed by Orlov V. N. [2], [3]. This article provides a summary of the results obtained in [4] to the complex region.

1. Orlov, Victor Nikolayevich Dr. of Phys. & Math. Sci., Professor, I. Yakovlev Chuvash State Pedagogical University, Cheboksary

2. Leonteva, Tatyana Yorevna Postgraduate Student, Department of Algebra, I. Yakovlev Chuvash State Pedagogical University, Cheboksary