Optimization of an a priori estimate of an analytical approximate solution of one class of nonlinear third order differential equation in the field of analytics

V. N. Orlov^a, A. Ya. Kornilov^b, A. V. Vorobyеva<sup>b

a</sup> Moscow State University of Civil Engineering
^b Moscow State University of Technologies and Managements

Abstract: The paper presents a solution to the problem of the influence of a disturbance of the initial data on the analytical an approximate solution of one class of nonlinear differential equations in the domain of analyticity. The results of the work allow us to carry out the analytical continuation of the solution of the considered class of nonlinear differential equation in the domain of analyticity. In this work, an a priori estimate of the analytical approximate solution is obtained and a technology for its optimization using an a posteriori error estimate is given. The results obtained are accompanied by numerical experiments.

Keywords: nonlinear differential equation, Cauchy problem, analytical approximate solution, a priori assessment, optimization.

Received: 01.06.2024
Revised: 18.12.2024
Accepted: 29.11.2024

DOI: 10.37972/chgpu.2024.60.2.003