Perturbation of initial data and analytical approximate solution of a class of nonlinear differential equations of the third order in the real domain

V. N. Orlov, A. M. Barzini

Moscow State University of Civil Engineering

Abstract: The paper presents a continuation of the previously obtained author's results. The dependence of the analytical approximate solution of one class of nonlinear differential equations on the perturbation of the initial data is established. A numerical experiment was carried out, confirming the theoretical results, and a variant of optimizing a priori estimates using a posteriori ones was also given. The presented results are the final stage in the substantiation of an analytical approximate solution for nonlinear differential equations that are generally not solvable in quadratures.

Keywords: Perturbation of initial data, analytical approximate solution, nonlinear differential equation, a priori and a posteriori estimates.

Received: 11.02.2023
Revised: 06.06.2023
Accepted: 05.05.2023

DOI: 10.37972/chgpu.2023.55.1.007