Integration of the Equation of the artificial Earth's Satellites Motion with Selection of Runge-Kutta-Fehlberg Schemes of Optimum Precision Order

TL;DR

This paper presents a method for numerically integrating satellite motion equations using optimized Runge-Kutta-Fehlberg schemes to ensure high local precision, demonstrated through numerical experiments in satellite dynamics.

Contribution

It introduces a new approach for selecting optimal Runge-Kutta-Fehlberg schemes based on specific criteria for satellite motion simulations.

Findings

Effective in achieving high local precision

Ensures global stability in satellite motion simulations

Suitable for multi-variable problems in simulation modeling

Abstract

An approach is treated for numerical integration of ordinary differential equations systems of the first order with choice of a computation scheme, ensuring the required local precision. The treatment is made on the basis of schemes of Runge-Kutta-Fehlberg type. Criteria are proposed as well as a method for the realization of the choice of an 'optimum' scheme. The effectiveness of the presented approach to problems in the field of satellite dynamics is illustrated by results from a numerical experiment. These results refer to a case when a satisfactory global stability of the solution for all treated cases is available. The effectiveness has been evaluated as good, especially when solving multi-variable problems in the sphere of simulation modelling.