Analytic Approximate Solution in the Neighborhood of a Moving Singular Point of a Class of Nonlinear Equations

Abstract

The paper considers a class of nonlinear differential equations which are not solvable in quadratures in general case. The author’s technology for solving such equations contains six problems. In this article, the solution to one of these problems is given, a real area in which it is possible to calculate an analytical approximate solution in the case of an approximate value of a moving singular point is obtained. Obtained results are based on the application of elements of differential calculus in finding estimates for the approximate solution error. Theoretical provisions are confirmed by numerical calculations, which characterize their reliability.

Keywords

• aspect of nonlinearity
• perturbation of a moving singular point
• real domain
• a-priori estimate