The boundary analogue of method of least squares for approximation of decision of (k+l)-regular generalized Dirichlet problem for elliptic differential equations arbitrary order in n-dimensional field was built in this work. Convergent and steady boundary analogue of method of collocation which possesses good computational characteristics was built on the basis of the boundary analogue of method of least squares and discretization of scalar product in Wm2(g). Proposed boundary analogues of variation methods take into account the order of a smoothness of data of boundary value problem 

In this paper full asymptotical decomposition of a high-frequent electro-magnetic field in chiral media is built. Recurrent formulas for coefficients of decomposition are founded. Polarization of electromagnetic waves are founded and explained in zero approximation 

The labour-consuming characters of finite element method is investigated by example of the first boundary problem for the ordinary differential second order equation. The elementary minimal splines are taken as a coordinate function. The estimate of the labour-consuming character of the solution of considered problem is obtained on the singleprocessor computer and on the parallel computational system (by the means of the concept of unlimited parallelism) 

A non-uniform bar moving in space under a tangential end force is considered. It is supposed that the bar can carry a nonstructural mass (a payload). This nonconservative system can lose stability by flutter or by divergence under certain conditions. Changing mass and/or stiffness distribution of the bar or nonstructural mass distribution we can influence the critical end force. Two optimization problems with critical follower load as a merit functional are studied, mass distributions of the bar and payload being taken as control functions. First we consider a bar without nonstructural mass. It is supposed that cross-sections of the bar are similar geometric figures and that the total mass of the bar is constant. It is necessary to find a mass distribution of the bar maximizing critical follower force. The mass distribution which significantly improves stability characteristics of the bar is obtained. Then a uniform bar carrying nonstructural mass is considered. We would like to maximize critical end force under the condition of total mass of the payload, assuming that admissible nonstructural mass distribution is a bounded function. With the use of Pontryagin's maximum principle it is shown that the optimal nonstructural mass distributions belong to the "bang-bang" type. Optimal solutions with two and four switching points are found. The problem of optimal displacement of a concentrated mass along the uniform bar is also considered. It is shown that the optimal solution is attained at the singularity of a boundary of the stability domain 

This work is examining the dynamics of elastic strip starting to move on the grainy plane without take-off from the state of static equilibrium. The upper foundation is pursed and moves with the given velocity. Various types of dependence friction of velocity are investigating. The regimes of tending to relative equilibrium and the regimes of relaxational and nonrelaxational oscillations are found. The results of this work agree with the results of the other researchers for more simple models and they are of more general character 

The problem of dynamic loading of a sample with the penny-shaped crack is investigated. Expressions for dynamic fracture toughness by means of the incubation-time criterion were received. It was shown that the diagrams of dependence of dynamic fracture toughness on time to fracture change qualitatively with the radius of penny-shaped crack 

This work presents the results of computational experiment at investigation of bifurcational effects and multiplicity of forms of axis-symmetric flow of incompressible fluid in gap between short cylinder internal of which is rotating. Methods of obtaining of decisions corresponding regular and irregular directions of meridional circulation in vortical cells are described. For some values of ratio of cylinder radiuses the maps of regimes at plane "non-dimentional height — Reynolds number" are plotting. The critical value of radial ratio is finding, below which existence of irregular modes are impossible 

The problem of finding of acoustic field of pointlike source in flat waveguide representing the infinite strip is considered. Functions which give the properties of the medium are considered faintly dependent from transverce co-ordinate. With using of Fourier method the problem is reduced to searching for set of decisions of Sturm – Liouville spectral problem. In the differential equation and boundary condditions the main parts are distinguished and the asymptoty of decision is being built with decreasing values of parameter. The question of uniform suitableness of this asymptoty is considered 

The investigation of gas dynamics of steady monoatomic and diatomic gas jet outflow from the supersonic nozzle of microthruster in vacuum has been carried out. The Direct Simulation Monte-Carlo (DSMC) method was used for the simulation. The influence of Reynolds numbers on the flowfield is analyzed. The special attention was paid to the flow in the vicinity of the nozzle lip and peripherical zone of the jet. The translational and rotational relaxation peculiarities behind the nozzle exit had been considered. The efficient algorithm of simulation for shared-memory multiprocessors is presented 

The direct Monte-Carlo simulation of axisymmetric steady gas flows in the inner atmosphere of a comet is presented in this work. The influence of rarefaction, non-uniform surface activity and small surface non-sphericity on the flow pattern is investigated. The special attention is paid to the boundary conditions on the surface of the cometary nucleus