Geodesic

Sommaire du Fascicule no. 1

Letter to editorial board
The features of gradient methods for distributed optimal-control problems
p. 3-21
The direct Lyapunov method in investigating the attraction of trajectories of finite-difference inclusions
p. 22-32
Application of the dynamic programming method to standardization problems
p. 33-42
Exact auxiliary functions in optimization problems
p. 43-57
The use of special transformations in the numerical solution of boundary layer problems
p. 58-71
On the existence of solutions of the contrast structure type
p. 72-86
A class of non-linear integral equations
p. 87-98
An iterative method of quasi-solution in problems of diffraction by dielectric bodies
p. 99-106
Investigation of problems of the diffraction of electromagnetic waves in locally non-uniform media
p. 107-121
Weighted estimate of the Monte-Carlo method for calculating the higher moments of the additive transport characteristics of multiplying particles
p. 122-134
On some difference-characteristic schemes for non-one-dimensional non-stationary problems in the theory of elasticity
p. 135-143
The use of local coordinates in optimization problems
p. 144-147
A method for the numerical solution of a system of ordinary differential equations of a quasichemical condensation model
p. 147-151
An investigation of the stability of certain two-layer difference schemes
p. 151-156
An alternative method for the numerical solution of the integrodifferential heat-conduction equation
p. 156-161
Analysis of transitional electromagnetic processes in wire antenna systems
p. 161-164
The general problem of stability analysis in linear programming
p. 164-167
A numerical method for solving Hill's equation in problems of quantum mechanics
p. 168-169
A method for solving diffraction problems
p. 169-171

Sommaire du Fascicule no. 2

Recursive interpolation by cubic splines with additional nodes
p. 179-185
Reinsch's method for solving the smoothing problem in several dimensions
p. 186-192
Computation of the maximum guaranteed payoff in dynamic models of conflict situations
p. 193-199
Estimation of the error in convex polynomial optimization problems
p. 200-216
Reduced-direction methods with feasible points in nonlinear programming
p. 217-230
The discrete $\Psi$-transformation method in integer programming
p. 231-242
A numerical-asymptotic multicomponent averaging method for equations with contrast coefficients
p. 243-253
Asymptotic behaviour of rapidly oscillating contrasting spatial structures
p. 254-269
Gyroscopic waves in media with time-dependent flow and rotation
p. 270-277
On the vibrations of a two-sided disc in a stratified fluid
p. 278-290
Investigation of an equation of electrophysics
p. 291-297
A priori estimates in problems of the synthesis of interference coverings
p. 298-309
Onsager reciprocal relationships for the motion of a rarified monatomic gas in an external field
p. 310-318
Localized solutions of a certain non-linear second-order differential equation
p. 319-320
A numerical algorithm for solving the Cauchy characteristic problem for ultrahyperbolic equations
p. 320-325
On the best one-layer clearing covering for a frequency interval
p. 325-327
The problem of the propagation of nonstationary acoustic waves in a relaxing medium
p. 328-332

Sommaire du Fascicule no. 3

Numerical canonical factorization algorithms and their application
p. 339-354
Approximately optimal algorithms for determining extrema in a certain class of functions
p. 355-365
A method for the asymptotic solution of singularly perturbed linear terminal control problems
p. 366-378
The complexity of the computation of the global extremum in a class of multi-extremum problems
p. 379-387
Approximation of the bounded solution of an ordinary linear differential equation by solutions of two-point boundary-value problems
p. 388-404
An asymptotic method for quasilinear vibrational systems with an aperiodic generating solution
p. 405-419
Programming a generalized cholesky algorithm for mixed discrete analogues of elliptic boundary-value problems
p. 420-429
Chebyshev acceleration of the Schwarz alternating process
p. 430-437
Accurate estimates for the amplitude and support of unbounded solutions of the nonlinear heat-conduction equation with a source
p. 438-448
A gradient procedure for intra-resonator control of light beams
p. 449-456
On an initial-boundary value problem which arises in the dynamics of a compressible stratified fluid
p. 457-465
Formulas for the approximate calculation of integrals over the whole plane
p. 466-470
The convergence in $W_2^2$ of a difference solution of the Dirichlet problem
p. 470-474

Sommaire du Fascicule no. 4

External estimates and construction of attainability sets for controlled systems
p. 483-490
The method of generalized stochastic gradient for solving minimax problems with constrained variables
p. 491-500
The flow of a heavy liquid in the presence of a periodic impressed force
p. 501-512
The best possible for the convergence of the semimixed finite element method for the main boundary-value problems of the theory of shallow shells in polygonal regions
p. 513-520
A collocation-grid method on moving grids for the numerical modelling of boundary layers
p. 521-534
Localized compression regimes in a heat-conducting gas
p. 535-547
Numerical modelling of pulsating regimes accompanying supersonic flow round a hollow cylinder
p. 548-556
On the solvability of plane-parallel problems in the theory of radiation transport
p. 557-569
Variational principles of the linear kinetic theory of a gas
p. 570-585
A numerical method of computing supersonic flows of a viscous gas
p. 586-600
The method of artificial viscosity for computing one-dimensional flows
p. 601-610
On the numerical solution of the Orr–Sommerfeld equation
p. 611-615
On the solvability of the problem of the development of a domain of turbulent homogeneous fluid
p. 616-619
Search for the maximum upper zero of a threshold function of multivalued logic
p. 620-622
Two methods for solving the problem of heat transfer in a rarefied gas
p. 623-626
On an implicit scheme with correction of flows for the numerical solution of Euler's equation
p. 626-628
Direct numerical integration of the Boltzmann equation for neutral gas mixtures
p. 628-629
The use of duality to determine the branching order of variables and to estimate the bounds in the solution of the knapsack problem
p. 630-631
Averaging of the stationary problem of heat conduction in a thin inhomogeneous plate
p. 632-634

Sommaire du Fascicule no. 5

On generalized discrepancy principle and generalized discrepancy method for $L$-pseudosolutions
p. 643-651
Construction of a single-step optimal stochastic algorithm for approximating a Lipschitz function
p. 652-662
Convex optimization with prescribed accuracy
p. 663-671
Monotonization of a family of implicit schemes
p. 672-679
Numerical solution of some quasilinear singularly perturbed heat-conduction equations on nonuniform grids
p. 680-696
Comparison of two-numerical methods for solving the problem of the diffraction of an $E$-polarized plane wave by an ideally conducting periodic surface
p. 697-704
Asymptotic representation of the solution of the problem of the propagation of acoustic waves in a non-uniform compressible relaxing medium
p. 705-715
Numerical solution of a quasilinear parabolic equation with a boundary layer
p. 716-726
Identification of a two-dimensional model of the flow of a homogeneous liquid in a porous medium
p. 727-735
Vibrations of a flat disk at the interface between two stratified liquids
p. 736-750
Energy characteristics of non-stationary internal waves in a vertical channel containing a stratified liquid
p. 751-766
Computation of viscous plasma heating under compression by a striker in a conical target
p. 767-779
Localization of the spectrum of eigenvalue problems nonlinear in the spectral parameter
p. 780-782
The multidimensional stationary phase method. The second term of the asymptotic expansions
p. 782-786
A decomposition approach to the solution of some integer programming problems with inexact data
p. 786-791
Convergence of the finite element method with one iteration
p. 791-796

Sommaire du Fascicule no. 6

Non-linear spectra of matrices and extremal problems
p. 803-816
Discrete approximation of extremal problems with operator inequality constraints
p. 817-825
Asymptotic error bounds in Galerkin approximation for a certain class of quasipotential equations
p. 826-836
The solution of systems of nonlinear equations of general form
p. 837-843
A mathematical programming problem with a convex irregular feasible set
p. 844-857
Asymptotic behaviour of the solution of the singularly perturbed parabolic problem in the critical case
p. 858-867
The mathematical structure of the solution of the equation $(\partial^2/\partial t^2)[u_{xx}-\beta^2u]+\omega^2_0u_{xx}=0$ and problems connected with it
p. 868-882
One-electron solitons in two-dimensional tunnelling structures
p. 883-893
Application of the incomplete Galerkin method for solving problems of the diffraction of electromagnetic waves by a nonhomogeneous cylinder
p. 894-909
Variational formulation of diffraction problems
p. 910-919
A method for solving kinetic equations of Fokker–Planck type for a plasma
p. 920-932
Numerical modelling of transverse flow round a cylinder based on the Euler equations
p. 933-940
A method of generating an interpolating curve with piecewise sign-constant curvature
p. 941-944
Chaplygin's method for the numerical solution of differential equations with retarded argument
p. 945-951
Viscous liquid flows that are independent of the Reynolds number
p. 951-955
Errata
Errata

Sommaire du Fascicule no. 7

Analysis of the error of the approximate superelement method
p. 963-983
The Pareto-optimality of Nash equilibrium in dynamic controlled systems with conflict
p. 984-996
Convergence properties of the gradient method under conditions of variable-level inference
p. 997-1007
Decomposition in extremal problems with special structure
p. 1008-1016
A step elimination method for the dynamic optimal inventory control problem
p. 1017-1030
The projection method for singularly perturbed boundary value problems
p. 1031-1044
A relationship between order and degree for a stable formula with advanced nodes
p. 1045-1056
A rigorous justification and estimation of the rate of convergence for the partial domain method in two-dimensional eigenvalue problems for the Laplace operator
p. 1057-1070
A non-linear boundary-value problem in the theory of radiation transfer
p. 1071-1080
Application of the method of generalized potentials to the solution of certain problems in the theory of the diffraction and propagation of waves
p. 1081-1092
On the approximation properties of an implicit difference scheme for the equations of gas dynamics
p. 1093-1102
The asymptotic forms of the solution of a non-linear problem for a singularly perturbed system of
p. 1103-1107
Some properties of discrete fuzzy sets
p. 1107-1112
Calculating the trajectory of a material particle in a two-dimensional (axisymmetric) conservative field
p. 1113-1115
Dmitrii Konstantinovich Faddeev (obituary)

Sommaire du Fascicule no. 8

Optimal cubature formulae for computing many-dimensional integrals of functions in the class $Q_{r,\gamma}(\Omega,1)$
p. 1123-1132
The maximum principle residual functional in optimal control theory
p. 1133-1149
The construction of a solution of the alternative linear programming problem
p. 1150-1156
Difference methods in problems of the optimal control of the stationary self-action of light beams
p. 1157-1169
Digital simulation of evolutionary stochastic differential equations
p. 1170-1179
An efficient method for calculating the emission current density in vacuum lines
p. 1180-1192
An iterative method for solving a problem of diffraction by a spherical segment
p. 1193-1200
The structure of the boundary layer of the plasma of the positive column of a glow discharge in electronegative gases
p. 1201-1209
A numerical method for solving the radiation transport equation in planar and spherical geometry
p. 1210-1223
Special features of difference schemes for solving the two-dimensional Navier–Stokes equations, connected with the formulation of the boundary conditions on the solid surface
p. 1224-1236
On the use of hybrid grid-characteristic schemes for the numerical solution of three-dimensional problems in the dynamics of a deformable solid
p. 1237-1244
Computer experiments to find the minimum lower unity of a monotone Boolean function
p. 1245-1256
An estimate of the rate of convergence of the discrepancy method for a linear programming problem with approximate data
p. 1257-1262
A method of finding the integral characteristics of attenuation factors for transfer equations
p. 1262-1267
An economical method for computing unsteady temporally non-local radiation conditions for waveguide systems
p. 1267-1271
Two-dimensional non-stationary flows of a viscous fluid
p. 1271-1272
Averaging of a problem in the elastic theory of a non-symmetric layered membrane
p. 1272-1273
Algorithms for solving a separable problem of discrete optimization
p. 1273-1275

Sommaire du Fascicule no. 9

Quasioptimal control search algorithms using state-space partitioning
p. 1283-1293
Approximating the measurement optimization problems for a parabolic system
p. 1294-1306
A numerical method of control optimization in delay systems for immune response modelling
p. 1307-1322
Discrete nonstationary radiation conditions for cylindrical systems. A convergence theorem
p. 1323-1331
Diffraction by a strip parallel to the surface of a compressible stratified liquid
p. 1332-1340
Determination of the absorption coefficient in the spherically symmetric case
p. 1341-1356
Increasing the order of approximation of Godunov's scheme using solutions of the generalized Riemann problem
p. 1357-1371
A version of the splitting method and implicit implementation of the boundary conditions for the solutions of the Navier–Stokes equations in curvilinear coordinates
p. 1372-1380
Methods for the simultaneous solution of the equations of gas dynamics and the kinetics of multiply-charged plasma
p. 1381-1393
Composite plates reinforced with high modulus fibres
p. 1394-1404
Approximation of conservation laws by high-resolution difference schemes
p. 1405-1417
An unsaturated method for the discretization of systems of linear differential equations implicit with respect to derivatives
p. 1418-1425
A difference scheme for a nonlinear singularly perturbed second order equation
p. 1425-1430
Combined recovery of the quadrupole splitting distribution function and the dependence of the isomer shift using Mössbauer spectral data
p. 1430-1434
Bratley P., Fox В., Schrage L. A guide to simulation. N. Y.: Springer, 1987. XXI+397 p. Book review
Vasilii Yakovlevich Arsenin (obituary)
p. 1435-1436

Sommaire du Fascicule no. 10

Determination and properties of optimal controls for a coordinated hierarchical system in the presence of uncontrolled disturbances
p. 1443-1453
Integer minimization of rational-separable functions
p. 1454-1466
An iterative decomposition method in single-stage stochastic integer-programming problems
p. 1467-1476
Convergence of difference schemes of the reference-operator method to generalized solutions of the axisymmetric Poisson equation
p. 1477-1486
The Korteweg–de Vries, Kadomtsev–Petviashvili and Boussinesq equations. Modulation theory
p. 1487-1501
Fundamental solutions and Green's formulae for families of equations arising in the theory of the oscillations of
p. 1502-1512
Structural properties of the solutions of the gravitational-gyroscopic wave equation and the explicit solution of a problem in the dynamics of a stratified rotating fluid
p. 1513-1525
On the stationary flow of a heavy fluid over an uneven, periodically varying bottom
p. 1526-1539
The solvability of the three-dimensional inverse problem for the non-linear Navier–Stokes equations
p. 1540-1552
A modified method of approximate factorization when calculating three-dimensional potential flows in channels
p. 1553-1570
Integrodifferential equations for non-spherical aerosols coagulation
p. 1571-1587
Optimal regularization of solutions of approximate stochastic systems of linear algebraic equations
p. 1588-1593
The influence of the “wrapping” effect on finding upper and lower estimates of solutions of systems of ordinary differential equations
p. 1593-1596
A method of increasing the stability of an implicit upwind scheme with three-point scalar pivotal condensations for Euler's equation
p. 1596-1599

Sommaire du Fascicule no. 11

Stability bounds for solutions of some conditionally well-posed problems on a set containing discontinuous functions
p. 1603-1613
The use of block symmetries to solve algebraic eigenvalue problems
p. 1614-1624
Computational complexity of generalized $K_N$-convolutions and the fast Vandermonde transform algorithm
p. 1625-1637
A new approach to the numerical solution of non-linear equations
p. 1638-1645
Approximation of bounded solutions and exponential dichotomy on the axis
p. 1646-1660
A method for the numerical solution of integral equations in boundary value problems with finite-order Abelian symmetry groups
p. 1661-1674
Numerical calculation of beams of charged particles by the method of iterations over subdomains
p. 1675-1688
The flow of electric current from rectilinear electrodes in a magnetized semiconductor film
p. 1689-1701
Methods of splitting by subdomains for the neutron transport equation
p. 1702-1718
A method for designing algorithms to compute viscous incompressible flows
p. 1719-1727
Representation of solutions of the two-dimensional gravitational-gyroscopic wave equation by generalized Taylor and Laurent series
p. 1728-1740
The properties of effective modulus of composition plates
p. 1741-1743
Analysis of the flow of a rarefied gas near the critical point
p. 1744-1749
A method of adapting grids
p. 1749-1752
Application of the resolving multipliers of the modified simplex method in problems of integer linear programming
p. 1753-1755
An iterative method for solving the coagulation equation with spatially inhomogeneous velocity fields
p. 1755-1757
Application of the Padé approximation to the solution of dynamic problems of the theory of elasticity for a space weakened by a plane crack
p. 1757-1758
Graham R., Knuth D., Patashnik О. Concrete mathematics: a foundation for computer science. Reading. Mass.: Addison-Weslev, 1989. XIII+625 p. Book review
Dagpunar J. Principles of random variate generation. Oxford: Clarendon Press, 1988. XVIII+228 p. Book review

Sommaire du Fascicule no. 12

Anatolii Alekseevich Dorodnitsyn (on the occasion of his eightieth birthday)
p. 1763-1764
Finite splitting algorithm for the $J$-symmetric generalized eigenvalue problem
p. 1765-1774
Some asymptotic formulae for cylindrical Bessel functions
p. 1775-1784
Non-local radiation conditions for the time-dependent Maxwell equations
p. 1785-1796
The multigrid method applied to a finite-element scheme for a two-dimensional Stokes-type system
p. 1797-1803
The formation of ordered vortex structures from unstable oscillations in the boundary layer
p. 1804-1814
Ablation of large meteor bodies under radiation heating
p. 1815-1826
Computation of functions in the algebra of triangular Toeplitz matrices and numerical inversion of the Laplace transform
p. 1827-1833
On an inertial flow
p. 1833-1834