Numerical Method of Integration on the Basis of Multidimensional Differential-Taylor Transformations

The paper presents a new numerical method integration for ordinary differential equations based on multidimensional differential-Taylor transformations. The method is designed to integrate differential equations whose right-hand side includes terms that are gradients of a potential function. A distinctive feature of the developed numerical-analytical method for integrating ordinary differential equations is that the calculation of accelerations in a differential equation is based on differential-Taylor transformations of various dimensions, while the calculation of the elements, used further in calculations based on one-dimensional differential-Taylor transformations, is made on the basis of multi-dimensional differential-Taylor transformations. The typical algorithm of a program for an explicit numerical scheme of integration by the developed method is proposed. The use of multidimensional differential-Taylor transformations reduces the methodological complexity of prescribing the initial data for developing a computerized integration procedure.