Integro-differential equations and functional analysis

Integration of equations of the two-body problem using a total polynomial system of partial differential equations

L. K. Babadzanjanz, I. Yu. Pototskaya, Yu. Yu. Pupysheva

St. Petersburg State University, St. Petersburg, Russian Federation

Abstract: The polynomial total system of partial differential equations constructed for the two-body problem is described in this paper. The algorithm for its numerical integration using the Taylor series method is presented. Recurrent formulas for Taylor coefficients obtained for the problem being solved are provided.

Keywords: two-body problem, Taylor Series Method, total polynomial PDE system, numerical PDE system integration.

UDC: 519.63, 521.1

MSC: 35F20, 65D30

Received: 25.09.2024
Revised: 31.01.2025
Accepted: 06.02.2025

DOI: 10.26516/1997-7670.2025.52.58