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

Currently, the differential equations are widely used in various fields of human activity [1] - [5]. The theory of linear differential equations is well developed [6] - [8], which is not true of the theory of nonlinear differential equations. Their development is hampered by moving singular points. In [9] - [12] proposed a method for the approximate solution of nonlinear differential equations with movable singularities, including the decision of six tasks. The first two problems: the formulation and proof of the existence and uniqueness of solutions of the nonlinear differential equation; construction of an approximate solution and investigation of the influence of the perturbation of the initial conditions for the approximate solution are presented in [13] - [14]. This paper presents a study of influence of the disturbance moving singular point on the approximate solution of nonlinear differential equations in the complex region. What is the continuation of the investigation [15]. The results are accompanied by estimates.

Leonteva, Tatyana Yorevna Post-graduate Student, Department of Mathematical analysis, Algebra and Geometry, I. Yakovlev Chuvash State Pedagogical University, Cheboksary