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The possibilities of the method for the numerical solution of high-order differential equations for solving tribology problems are shown. In particular, the problem of deformation of a section of a wheel during rolling is considered, taking into account the contact zone. The technique for solving the problem is based on the general use of the parameter continuation method and the Newton-Kantorovich method, it describes the spatial nonlinear deformation of an elastic element of arbitrary curvature with an arbitrary vector of acting static or quasi-static loads, while this article considers only the plane problem. Methods of representation of loads on the section under consideration are given. Also considered is the consideration of the variability of the line of contact of the wheel, depending on its deformation. To illustrate the method, an example of solving the problem from determining the stress-strain state of a wheel during rolling is given, taking into account the plane of contact with the supporting surface. The given graphs are built automatically using application programs that solve the problem. The described algorithms allow, in contrast to the previously known ones, to solve fundamentally new types of problems of elastic deformation of triboconjugation elements, to unify the types of structures that are investigated, to efficiently switch from one design scheme to another depending on physical and geometric parameters and load conditions, to obtain output data in user-friendly form. Determination of the factors that affect the provision of the established parameters of the tribo-conjugation and the establishment of ways of purposeful management of these factors will reduce and optimize the study to improve their quality. [ABSTRACT FROM AUTHOR]

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