Research of a third-order nonlinear differential equation in the vicinity of a moving singular point for a complex plane

Abstract

This article generalizes the previously obtained results of existence and uniqueness theorems for the solution of a third-order nonlinear differential equation in the vicinity of moving singular points in the complex domain, as well as constructs an analytical approximate solution, and obtains a priori estimates of the error of this approximate solution. The study was carried out using the modified method of majorants to solve this equation, which differs from the classical theory, in which this method is applied to the right-hand side of the equation The final point of the article is to conduct a numerical experiment to test the theoretical positions obtained.