Modeling of Solving Stabilized Differential Equations By Differential-Taylor Transformations

The paper presents a typical algorithm for numerical integration of the ordinary differential equation stabilized by the Baumgart method. The integration is performed on the basis of Pukhov’s differential-Taylor transformations. Constant step size and order integration, as well as with “by steps”, “by steps and order” adaptation are considered. For adaptation, in addition to the traditional approach, which deals with providing a given relative error according to the phase variables of integration, an approach, which deals with providing a given relative error according to the integral of the original differential equation adopted for stabilization by the Baumgart method is proposed. A practical example of integrating the differential equation of spacecraft motion is considered. The proposed algorithm can be effectively used in the development of programs for computer integration of ordinary differential equations.