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

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