Showing papers in "Ussr Computational Mathematics and Mathematical Physics in 1975"
TL;DR: In this article, the values of the nodes and weights of Gauss-Markov quadrature formulae for integration over the surface of a three-dimensional sphere, from 9-th up to and including the 17-th order, invariant under the octahedron group are given.
Abstract: TABLES are given for the values of the nodes and weights of Gauss-Markov quadrature formulae for integration over the surface of a three-dimensional sphere, from 9-th up to and including the 17-th order, invariant under the octahedron group.
157 citations
TL;DR: A proof of the global existence of a weak solution of Vlasov's system of equations describing the evolution of the density distribution of a two-component plasma is given in this article.
Abstract: A PROOF is given of the theorem of the global existence of a weak solution of Vlasov's system of equations describing the evolution of the density distribution of a two-component plasma.
127 citations
72 citations
TL;DR: In this article, a numerical method of solving problems of the dynamics of a viscous incompressible fluid, using the splitting of the non-stationary equations of motion, first proposed by Harlow and Chorin is considered.
Abstract: A NUMERICAL method of solving problems of the dynamics of a viscous incompressible fluid, using the splitting of the non-stationary equations of motion, first proposed by Harlow and Chorin is considered. Unlike methods of the MAC type and its modifications (SMAC, MACRL, ALE etc), the difference scheme of the proposed method enables us to calculate flows without using the boundary condition for the vortex or the pressure on the solid surface. Some results of numerical calculations of the flow past bodies of finite dimensions are given which illustrate the possibilities of the method.
58 citations
54 citations
31 citations
TL;DR: The extrema of the radius of stability are found, and upper and lower bounds are obtained for it.
Abstract: THE IDEA of the radius of stability for the distance matrix of the travelling salesman problem is introduced, and an analytic expression is obtained for it. The extrema of the radius of stability are found, and upper and lower bounds are obtained for it.
23 citations
TL;DR: In this article, a numerical method for constructing sets of attainability for linear systems with phase constraints of the bottleneck type is described, which is based on replacing the differential system by a difference system.
Abstract: A NUMERICAL method is described for constructing sets of attainability for linear systems with phase constraints of the bottleneck type. The method is based on replacing the differential system by a difference system and constructing the sets of attainability for the difference system by finding the conjugate is examined. A computational example is given.
23 citations
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21 citations
TL;DR: In this article, generalization of the method of Lympunov functions is outlined, whereby the convergence of numerical methods of optimization may be proved, and theorems on sufficient conditions on convergence of continuous and discrete schemes are stated and proved.
Abstract: GENERALIZATIONS of the method of Lympunov functions are outlined, whereby the convergence of numerical methods of optimization may be proved. Theorems on sufficient conditions for the convergence of continuous and discrete schemes are stated and proved. The application of the theorems is illustrated by examples.
TL;DR: In this paper, an iterative method based on the use of the conservation differential equations is proposed for the numerical solution of stationary problems at moderate and low knudsen numbers, where the problems of heat conduction, Couette flows and shock wave structure are solved.
Abstract: THE INVESTIGATION is based on a model kinetic equation. An iterative method based on the use of the conservation differential equations is proposed for the numerical solution of stationary problems at moderate and low knudsen numbers. The problems of heat conduction, Couette flows and shock wave structure are solved for the whole range of Knudsen numbers as examples of the use of the method. The method is most efficient for low Knudsen numbers.
TL;DR: In this article, a bounded value problem in a bounded region whose solution approximates the solution of the problem is discussed and the effect of boundary conditions, specified on an additional distant boundary, is investigated.
Abstract: A BOUNDARY value problem in a bounded region, whose solution approximates the solution of the problem is discussed. The effect of boundary conditions, specified on an additional distant boundary, is investigated. A numerical solution algorithm is described and the results of calculations for Re = 18 to 100 are presented.
TL;DR: In this article, an exact solution of a non-linear integro-differential equation for describing turbulent diffusion is found, and the physical significance of the solution obtained is analyzed in spaces of one, two and three domensions.
Abstract: AN EXACT solution of a non-linear integro-differential equation is found. It is shown that this equation is a model equation for describing turbulent diffusion, and in this connection the physical significance of the solution obtained is analysed in spaces of one, two and three domensions.
TL;DR: In this paper, the penetration of radiation into a half-space occupied by matter at a constant temperature and with an absorption coefficient dependent on frequency only was checked using two different methods.
Abstract: TWO METHODS, due to the authors, are used to check the penetration of radiation into a half-space occupied by matter at a constant temperature and with an absorption coefficient dependent on frequency only. The erros of the calculation are obtained for three versions of the relation between the frequency and the intensity of the external radiation.
TL;DR: In this paper, a method of solution on a sequence of nets is used to solve non-linear free convection equations, consisting of the Navier-Stokes equations and the heat conduction equation.
Abstract: A METHOD of solution on a sequence of nets is used to solve non-linear free convection equations, consisting of the Navier-Stokes equations and the heat conduction equation. From the literature the use of this method is known only for the solution of linear equations of elliptic type [l-S]. The method gives an economy of computer time by a factor of 3 to 5 compared with the method on a fmed net and enables the error of the solution to be estimated.
TL;DR: In this article, a numerical computing scheme for the transfer equation is proposed which is suitable for any optical dimensions of the difference net and the errors are analysed. But the scheme is not suitable for the case when the optical dimension of the net is increased.
Abstract: A NUMERICAL computing scheme for the transfer equation is proposed which is suitable for any optical dimensions of the difference net. The errors are analysed. Examples are given of numerical schemes giving a false result when the optical dimensions of the net are increased.