About the authors
| First name, Middle name, Last name, Scientific degree, Scientific rank, Current position. Full and brief name of the organization, The organization address. | Gorskaya T.Iu. – candidate of technical sciences, associate professor E-mail: This e-mail address is being protected from spambots. You need JavaScript enabled to view it Kazan State University of Architecture and Engineering The organization address: 420043, Russia, Kazan, Zelenaya st., 1 Ozhegova A.V. – candidate of physical-mathematical sciences, associate professor E-mail: This e-mail address is being protected from spambots. You need JavaScript enabled to view it Kazan (Volga) Federal University The organization address: 420008, Russia, Kazan, Kremlevskaya st., 18 |
| Title of the article | On the convergence of the projection method for an equation of the goals of the movement |
| Abstract. | Work is devoted to theoretical justification with the subsequent numerical solution of a problem of movement. This research is conducted within hydrodynamics studying in axisymmetric channels for the purpose of creation of channels for the highly effective heat exchange equipment. The mathematical apparatus allows to find out the hydrodynamic picture arising in flowing channels of various configurations for optimization of a profile of channels, for the purpose of improvement of a hydrodynamic picture. In work the approximate solution of the equation of Navier-Stokes is investigated. As functional space the space of the functions possessing the second generalized derivative from a class of square and summable functions is taken. The analysis of existing approaches to justifications and solutions of the initial equation is submitted. Using a method of monotonous operators, the general theory of approximate methods, existence and uniqueness of the approximate decision received by a projective method is established. The power space in which scalar work and norm were set was entered for this purpose. Convergence of the approximate decision to the exact decision on norm of power space in terms of the best mean square approach is proved. |
| Keywords. | Regional tasks, numerical methods, generalized solution, speed of convergence of an approximate method. |
| For citations: | Gorskaya T.Iu., Ozhegova A.V. On the convergence of the projection method for an equation of the goals of the movement // Izvestiya KGASU. 2013. №2(24) P.175-179. |
