### Software

In the section presented complex program procedures, written in different programming languages and in a variety of computer algebra systems, that allow to solve actual scientific tasks.

Yu.G. Ignat'ev, A.R. Samigullina

Software environment: Maple

The described software complex for numerical modeling of nonlinear dynamic systems. The formation of solutions in the format of spline allows you to apply analytical techniques for the study of dynamical systems.

Yu.G. Ignat'ev, A.A. Agathonov

Software environment: Maple

Package GravPerturbations allows to calculate in analytical form the basic geometry of the relativistic theory of gravity in the second order in the perturbations relative to the unperturbed gravitational field: Einstein tensor, \(G_{ik}\), the Ricci tensor, \(R_{ik}\) and scalar curvature \(R\).

Yu.G. Ignat'ev, A.A. Agathonov

Software environment: Maple 18 or latter

The package **EquiSurface** carries out the construction of equidistant equipotential surfaces and gradient lines to it for a given potential function in three-dimensional space in applied mathematical package Maple. The package contains a single command, **equipotential**, input parameters which are: the potential function, the number of equipotential surfaces and the area of space. Additional program parameters that determine the graphic presentation of results are the image type of the surface (dots, mesh surface or translucent smooth surface)/of its cross section. When choosing special values of the parameter to obtain two-dimensional cross sections of the equipotential surfaces and gradient lines to him in any plane parallel to the coordinate planes. A special option allows also displayed in the header of the graphical object a mathematical formula specified potential. The program is designed for researchers in the area of field theory and mathematical modeling and system of education of Russia.

Yu.G. Ignat'ev, M.L. Mikhailov

Software environment: Maple

The software package is designed for the automated ordering two, three, four and five-dimensional arrays on the first (the first two) elements that are based on their three-dimensional arrays of functions of one and two variables and the subsequent construction of the parameterized line (surface) formatted array displays the results in the form of two (three) dimensional charts with adjustable parameters in Maple computer mathematics system.

Yu.G. Ignat'ev, A.R. Samigullina

Software environment: Maple

The package **DifEqTools** created based on earlier copyright packages **DifEq** and **Splines** and allows to solve numerically the system of ordinary differential equations (odes), **solved with respect to higher-order derivatives**. When this command packet is output to the numerical solution of the system in functional form \(y_i(t)\), requiring no additional software procedures for implementation.

The software package **DifEqTools** allows us to represent the numerical solution in the form of splines, which allows to treat the obtained solutions, as with conventional analytical functions, including, for example, to differentiate and integrate those decisions with a simple command and the result again is to provide, in a spline form (i.e., in the form of a piecewise-defined function consisting of polynomials).

The package **DifEqTools** created based on earlier copyright packages **DifEq** and **Splines** and allows you to automatically withdraw a graphic representation of 2d and 3d, static and dynamic charts, built as numeric, and spline solutions of nonlinear systems of ODE of any order with the graphs of any unknown functions and all their derivatives. The coordinate axes are automatically numbered.

E.V. Chebotareva

Software environment: Maple

Package ConvEq allows to solve convolution equations in the space of distributions with one-sided bounded support.