Dependence of the Analytical Approximate Solution to the Van der Pol Equation on the Perturbation of a Moving Singular Point in the Complex Domain

Abstract

This paper considers a theoretical substantiation of the influence of a perturbation of a moving singular point on the analytical approximate solution to the Van der Pol equation obtained earlier by the author. A priori estimates of the error of the analytical approximate solution are obtained, which allows the solving of the inverse problem of the theory of error: what should the structure of the analytical approximate solution be in order to obtain a result with a given accuracy? Thanks to a new approach for obtaining a priori evaluations of errors, based on elements of differential calculus, the domain, used to obtain an analytical approximate solution, was substantially expanded. A variant of optimizing a priori estimates using a posteriori estimates is illustrated. The results of a numerical experiment are also presented.

Nonlinear Differential Equations of Flow Motion Considering Resistance Forces

“…This paper represents the experimental data obtained by the Department of Hydraulic Engineering and Melioration of the Don State Agrarian University. This work is the development of analytical methods for solving problems of technical mechanics of liquids and gases [1,17,19], using a technique for solving nonlinear problems similar to those proposed in [24][25][26][27][28][29][30].…”

Mathematical Calculation of Synchronous Electric Motors Dynamic Stability

“…Equation ( 9) is nonlinear with respect to ω(t). If A depends on t, then the author's analytical approximate solution method is needed [26][27][28][29][30][31]. In the case when A does not depend on t, we can consider t(ω) which is the inverse function for ω(t) and, taking into account the initial conditions ω(0) = 1, t(1) = 0, it is possible to solve the Equation ( 9) in quadratures.…”