显示样式： 排序： IF:  GO 导出

Inverse Problems of Natural Science Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200801
S. I. KabanikhinAbstract A brief definition of inverse and illposed problems is given, the history of studying such problems is presented, and the relations of inverse problems to computer simulation is discussed.

Asymptotic Solution of Coefficient Inverse Problems for BurgersType Equations Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200801
V. T. Volkov, N. N. NefedovAbstract For a singularly perturbed reaction–diffusion–advection equation, called in applications a Burgerstype equation and having a timeperiodic solution with an internal transition layer, asymptotic analysis is used to solve some inverse problems of reconstructing model parameters (determining the linear amplification factor and boundary conditions) from known information about the observed solution

Reconstruction of Magnetic Susceptibility Using Full Magnetic Gradient Data Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200801
Y. Wang, I. I. Kolotov, D. V. Lukyanenko, A. G. YagolaAbstract The paper discusses the specificities of solving the inverse problem of reconstructing the magnetic susceptibility using complete tensor magnetic gradient data. This problem reduces to solving a system of two threedimensional Fredholm integral equations of the first kind, one of which relates the magnetic susceptibility of a bounded body to the magnetic field induced by it and the other,

Phaseless Inverse Problems for Schrödinger, Helmholtz, and Maxwell Equations Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200801
V. G. RomanovAbstract A survey of recent research concerning phaseless inverse problems for several differential equations is given. Mainly, the surveyed studies were performed over the last five years, although their importance of this subject for quantum scattering theory was noted more than 40 years ago. Problem formulations and results are presented, and the basic ideas underlying the research are described

Computational Approach to the Investigation of the Error SelfCompensation Effect in the Deposition of Multilayer Optical Coatings Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200801
I. V. Kochikov, A. V. Tikhonravov, A. G. YagolaAbstract A new computational approach is developed to evaluate the strength of the error selfcompensation effect in the case of broadband optical monitoring of the multilayer coating deposition process. A new form of estimating the strength of the error selfcompensation effect is suggested. Computational experiments simulating the deposition process are used to study the presence of the selfcompensation

Application of Neural Networks in Nonlinear Inverse Problems of Geophysics Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200801
E. A. Obornev, I. E. Obornev, E. A. Rodionov, M. I. ShimelevichAbstract Neural networks (NN) are widely used for solving various problems of geophysical data interpretation and processing. The application of the neural network approximation (NNA) method for solving inverse problems, including inverse multicriteria problems of geophysics that are reduced to a nonlinear operator equation of first kind (respectively, to a system of operator equations) is considered

An Algorithm for Recovering the Characteristics of the Initial State of Supernova Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200801
S. I. Kabanikhin, I. M. Kulikov, M. A. ShishleninAbstract An optimization method for the numerical solution of the inverse problem of recovering the initial state of a supernova is proposed. The gradient of the inverse problem objective functional is constructed. The solution of the direct and adjoint problems is based on a combination of the large particle method, Godunov’s method, and piecewise parabolic method on a local stencil. Results of the

ExtraOptimal Methods for Solving IllPosed Problems: Survey of Theory and Examples Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200801
A. S. LeonovAbstract A new direction in methods for solving illposed problems, namely, the theory of regularizing algorithms with approximate solutions of extraoptimal quality is surveyed. A distinctive feature of these methods is that they are optimal not only in the order of accuracy of resulting approximate solutions, but also with respect to a userspecified quality functional. Such functionals can be specified

Direct and Converse Theorems for Iterative Methods of Solving Irregular Operator Equations and Finite Difference Methods for Solving IllPosed Cauchy Problems Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200801
A. B. Bakushinskii, M. Yu. Kokurin, M. M. KokurinAbstract Results obtained in recent years concerning necessary and sufficient conditions for the convergence (at a given rate) of approximation methods for solutions of irregular operator equations are overviewed. The exposition is given in the context of classical direct and converse theorems of approximation theory. Due to the proximity of the resulting necessary and sufficient conditions to each

Numerical Solution of an Inverse Multifrequency Problem in Scalar Acoustics Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200801
A. B. Bakushinskii, A. S. LeonovAbstract A new algorithm is proposed for solving a threedimensional scalar inverse problem of acoustic sensing in an inhomogeneous medium with given complex wave field amplitudes measured outside the inhomogeneity region. In the case of data measured in a “plane layer,” the inverse problem is reduced via the Fourier transform to a set of onedimensional Fredholm integral equations of the first kind

Iterative Fejér Processes in IllPosed Problems Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200801
V. V. VasinAbstract A brief survey is given concerning iterative processes of Fejér type for basic statements of illposed problems, including constrained quadratic and convex minimization problems, variational inequalities, and linear and nonlinear operator equations in Hilbert spaces. By applying the method of successive approximations and its modification using correction factors, all these statements reduce

Inverse Problem of Electrodynamics for Anisotropic Medium: Linear Approximation Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200801
V. G. RomanovAbstract For electrodynamic equations with permittivity specified by a symmetric matrix \(\varepsilon (x) = ({{\varepsilon }_{{ij}}}(x),i,j = 1,2,3)\), the inverse problem of determining this matrix from information on solutions of these equations is considered. It is assumed that the permittivity is a given positive constant \({{\varepsilon }_{0}} > 0\) outside a bounded domain \(\Omega \subset {{\mathbb{R}}^{3}}\)

On Zeros of the Modified Bessel Function of the Second Kind Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200630
S. M. Bagirova, A. Kh. KhanmamedovAbstract Zeros of the modified Bessel function of the second kind (Macdonald function) \({{K}_{\nu }}\left( z \right)\) considered as a function of the index \(\nu \) are studied. It is proved that, for fixed \(z,\,z > 0\), the function \({{K}_{\nu }}\left( z \right)\) has a countable number of simple purely imaginary zeros \({{\nu }_{n}}\). The asymptotics of the zeros \({{\nu }_{n}}\) as \(n \to

Analysis of the QuasiTransfer Approximation in Problems with Analytical Solution Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200630
A. A. ShestakovAbstract The quasitransfer approximation reduces the numerical solution of the kinetic equation to solving the diffusion equation through introducing correction factors. The transition to the diffusion equation simplifies the numerical solution of the kinetic equation and makes it possible to use monotonic schemes of the second order of accuracy in solving problems of radiative heat transfer. In this

Numerical Algorithms for Systems with Extramassive Parallelism Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200630
V. P. Osipov, B. N. ChetverushkinAbstract Difficulties associated with ultrahighperformance computer systems that will appear in the near future and possible ways of their solution are discussed. Examples of simulating magnetogasdynamics problems are given.

Mathematical Modeling of Spot Dynamics in a Stratified Medium Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200630
V. A. Gushchin, I. A. SmirnovaAbstract The investigation of dynamics of mixed fluid spots in a stratified environment is of interest both for the study of the ocean fine structure and for the study of wake dynamics behind moving underwater objects. The paper is devoted to the construction of a physical and mathematical model for this problem. Salinity is used as the stratifying component. This model is described by the Navier–Stokes

Singular Points and Asymptotics in the Singular Cauchy Problem for the Parabolic Equation with a Small Parameter Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200630
S. V. ZakharovAbstract The results obtained by Il’in and his school concerning the asymptotic behavior of solutions to the Cauchy problem for the quasilinear parabolic equation with a small parameter multiplying the higher order derivative in the vicinity of singular points are presented. The equation under examination is of interest because it provides a model of the propagation of nonlinear waves in dissipative

Use of Projective Coordinate Descent in the Fekete Problem Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200630
B. T. Polyak, I. F. FatkhullinAbstract The problem of minimizing the energy of a system of \(N\) points on a sphere in \({{\mathbb{R}}^{3}}\), interacting with the potential \(U = \tfrac{1}{{{{r}^{s}}}}\), \(s > 0\), where \(r\) is the Euclidean distance between a pair of points, is considered. A method of projective coordinate descent using a fast calculation of the function and the gradient, as well as a secondorder coordinate

Parallel MosaicSkeleton Algorithm for the Numerical Solution of a ThreeDimensional Scalar Scattering Problem in Integral Form Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200630
A. A. Kashirin, S. I. Smagin, M. Yu. TimofeenkoAbstract A threedimensional scalar stationary scattering problem is considered. It is formulated in the form of a weakly singular Fredholm boundary integral equation of the first kind with a single unknown function. The equation is approximated by a system of linear algebraic equations, which is then solved numerically by an iterative method. The mosaicskeleton method is used at the stage of the

Numerical Solution of Linear Differential Equations with Nonlocal Nonlinear Conditions Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200630
K. R. AidazadeAbstract The numerical solution of systems of linear ordinary differential equations with nonlocal nonlinear conditions depending on the values of the desired function at intermediate points is investigated. Conditions for the existence of a solution to the problem under consideration are given. For the numerical solution, an approach is proposed that reduces the problem to two auxiliary linear systems

On the Accuracy of Bicompact Schemes as Applied to Computation of Unsteady Shock Waves Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200630
M. D. Bragin, B. V. RogovAbstract Bicompact schemes that have the fourth order of classical approximation in space and a higher order (at least the second) in time are considered. Their accuracy is studied as applied to a quasilinear hyperbolic system of conservation laws with discontinuous solutions involving shock waves with variable propagation velocities. The shallow water equations are used as an example of such a system

Estimates of the Deviation from Exact Solutions of Boundary Value Problems in Measures Stronger than the Energy Norm Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200630
S. I. RepinAbstract The paper is concerned with estimates of the difference between a given function and the exact solution of an elliptic boundary value problem. Estimates of this type have been derived earlier in terms of the natural energy norm. In this work, an approach is proposed to obtain stronger measures of the deviation and relevant estimates applicable if the exact solution and the approximation have

Gaussian Functions Combined with Kolmogorov’s Theorem as Applied to Approximation of Functions of Several Variables Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200630
A. V. ChernovAbstract A special class of approximations of continuous functions of several variables on the unit coordinate cube is investigated. The class is constructed using Kolmogorov’s theorem stating that functions of the indicated type can be represented as a finite superposition of continuous singlevariable functions and another result on the approximation of such functions by linear combinations of quadratic

TwoDimensional Stationary Thermocapillary Flow of Two Liquids in a Plane Channel Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200630
V. K. Andreev, E. N. LemeshkovaAbstract The problem of twodimensional stationary flow of two immiscible liquids in a plane channel with rigid walls is studied. On the one of walls a temperature distribution is imposed and the another wall is heatinsulated. On the common interface the interfacial energy change is taken into account. The temperature in the liquids is distributed according to a quadratic law. It agrees with velocities

Symmetrization of MHD Equations of Incompressible Viscoelastic Polymer Fluid Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200630
A. M. Blokhin, A. Yu. GoldinAbstract Equations describing the flow of an incompressible viscoelastic polymer fluid in the presence of a magnetic field are considered. The symmetrization of this system of equations is discussed.

S.K. Godunov and Kinetic Theory at the Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200608
S. Z. Adzhiiev, Ya. G. Batishcheva, V. V. Vedenyapin, Yu. A. Volkov, V. V. Kazantseva, I. V. Melikhov, M. A. Negmatov, Yu. N. Orlov, N. N. Fimin, V. M. ChechetkinAbstract The history of the cooperation between the staff of the Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences and S.K. Godunov is described. Numerous novel and interesting results in the theory of kinetic equations and computational mathematics were obtained in the course of this cooperation.

Method of Difference Potentials for Evolution Equations with Lacunas Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200608
S. V. Petropavlovsky, S. V. TsynkovAbstract A boundary method for computing unsteady wave propagation in threedimensional space is proposed. The described approach is based on the method of difference potentials and the Huygens principle, which makes it possible to update the solution on the scatterer boundary by using a fixed time interval.

Optimization Methods for Solving Inverse Immunology and Epidemiology Problems Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200608
S. I. Kabanikhin, O. I. KrivorotkoAbstract Inverse problems for systems of nonlinear ordinary differential equations are studied. In these problems, the unknown coefficients and initial data must be found given additional information about the solution to the corresponding direct problems; this information is obtained by measurements made at some specified points in time. Examples of inverse immunology and epidemiology problems arising

On the Existence and Uniqueness of the Solution to the Cauchy Problem for a System of Integral Equations Describing the Motion of a Rarefied Mass of a SelfGravitating Gas Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200608
N. P. ChuevAbstract The Cauchy problem for a system of nonlinear Volterratype integral equations that describes, in Lagrangian coordinates, the motion of a finite mass of a rarefied selfgravitating gas bounded by a free surface is studied. A theorem of the existence and uniqueness of a solution to the problem in the space of infinitely differentiable functions is proved. The solution is constructed in the form

Numerical Method of QuasiIsometric Parametrization for TwoDimensional Curvilinear Domains Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200608
S. K. Godunov, V. T. Zhukov, O. B. FeodoritovaAbstract A method for constructing a quasiisometric parametrization of a plane curvilinear quadrilateral is described. The parametrization is defined using a generalized Dirichlet variational functional. Based on its minimization, an algorithm for generating grids that implement a quasiisometric parametrization of quadrilaterals with curved, but sufficiently smooth boundaries is developed. Primary

Thermodynamic Consistency and Mathematical WellPosedness in the Theory of Elastoplastic, Granular, and Porous Materials Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200608
V. M. SadovskiiAbstract Mathematical models of the dynamics of elastoplastic, granular, and porous media are reduced to variational inequalities for hyperbolic differential operators that are thermodynamically consistent in the sense of Godunov. On this basis, the concept of weak solutions with dissipative shock waves is introduced and a priori estimates of smooth solutions in characteristic conoids of operators

Optimization of a FiniteDifference Scheme for Numerical Solution of the Helmholtz Equation Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200608
V. I. Kostin, S. A. Solov’evAbstract In this article, we propose an optimization method for a difference scheme for the numerical solution of the Helmholtz equation, applicable for any ratio of the grid steps. In the range of the number of points per wavelength of practical interest, the dispersion error of the optimal scheme is comparable with the error of higher order schemes known in the literature.

Stability of OneDimensional Steady Flows with Detonation Wave in a Channel of Variable CrossSectional Area Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200608
Kh. F. Valiyev, A. N. Kraiko, N. I. TillyayevaAbstract The stability of onedimensional steady flows of an ideal (inviscid and nonheatconducting) gas in channels of variable cross section with combustion in a structurally stable detonation wave is studied. The detonation wave represents a discontinuity surface propagating normally to the axis of the channel. It was previously established that, in this formulation, steady flows with combustion

Study of Entropy Properties of a Linearized Version of Godunov’s Method Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200608
S. K. Godunov, V. V. Denisenko, D. V. Klyuchinskii, S. V. Fortova, V. V. ShepelevAbstract The ideas of formulating a weak solution for a hyperbolic system of onedimensional gas dynamics equations are presented. An important aspect is the examination of the scheme for the fulfillment of the nondecreasing entropy law, which must hold for weak solutions and is obligatory from a physics point of view. The concept of a weak solution is defined in a finitedifference formulation with

Application of the Nesvetay Code for Solving ThreeDimensional HighAltitude Aerodynamics Problems Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200608
V. A. TitarevAbstract A survey of the capabilities of the Nesvetay code as applied to computing the flow of a highspeed monatomic gas around objects of irregular shape for large flight altitudes is given. An implicit numerical method on an arbitrary unstructured grid and a twolevel approach to the organization of parallel computations are described. This code is compared with the wellknown MONACO and SMILE codes

On Linear Instability of the State of Rest of an Incompressible Polymer Fluid in the Presence of Strong Discontinuity Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200608
A. M. Blokhin, R. E. SemenkoAbstract A linear problem of small perturbations of the flow of immiscible polymer fluids in a flat channel is formulated. For this problem, the existence of solutions unlimitedly increasing with time, the presence of which means linear instability of the state of rest of a polymer fluid with a strong discontinuity, is studied.

Estimates for Exponential Decay of Solutions to One Class of Nonlinear Systems of Neutral Type with Periodic Coefficients Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200608
I. I. MatveevaAbstract The class of nonlinear systems of delay differential equations with periodic coefficients in linear terms is considered. By using a special class of Lyapunov–Krasovskii functionals, conditions for the exponential stability of the zero solution are indicated and estimates characterizing the rate of exponential decay of solutions at infinity are obtained.

Generalized Solutions of the Galilean Invariant Thermodynamically Compatible Conservation Laws Constructed Using Godunov’s Ideas Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200608
M. Ya. Ivanov, V. K. MamaevAbstract The Galilean invariant thermodynamically compatible conservation laws that admit a class of generalized solutions is analyzed. The main feature of the generalized solutions considered in this paper is that they describe smooth solutions with the kinetic energy and total pressure loss, which accompany the dynamic process of heat supply. The principal properties of the generalized solutions

Cauchy Problem for One Pseudohyperbolic System Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200608
L. N. Bondar, G. V. Demidenko, G. M. PintusAbstract The Cauchy problem for one pseudohyperbolic system is considered. The unique solvability of this problem in Sobolev spaces is proved. Systems of this type arise in describing wave dynamics in rods.

Superconvergent Algorithms for the Numerical Solution of the Laplace Equation in Smooth Axisymmetric Domains Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200608
V. N. BelykhAbstract A fundamentally new—nonsaturable—method is constructed for the numerical solution of elliptic boundary value problems for the Laplace equation in \({{C}^{\infty }}\)smooth axisymmetric domains of fairly arbitrary shape. A distinctive feature of the method is that it has a zero leading error term. As a result, the method is automatically adjusted to any redundant (extraordinary) smoothness

Generalized and Variational Statements of the Riemann Problem with Applications to the Development of Godunov’s Method Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200608
I. S. MenshovAbstract This paper is devoted to the numerical method for solving the fluid dynamics equations proposed by Godunov more than 60 years ago. This method is an explicit finite volume firstorder discretization of the system of balance differential equations with the approximation of the numerical flux on the faces of the computational cells based on the exact solution of the Riemann problem. Statements

On the Stability of Plasma Equilibrium in the Neighborhood of a Straight Current Conductor Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200608
K. V. Brushlinskii, S. A. Krivtsov, E. V. StepinAbstract The article presents a mathematical model of an equilibrium magnetoplasma configuration in a plasma cylinder containing on its axis a conductor of finite diameter with a current creating a magnetic field confining the plasma. The annular configurations considered here are the simplest elements of a wide class of galatea traps with conductors immersed in the plasma volume. The problems concerning

Problems on a Semiaxis for an IntegroDifferential Equation with Quadratic Nonlinearity Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200608
V. L. VaskevichAbstract A functional equation is considered in which a linear combination of a twovariable function and its time derivative is set equal to the double integral of a quadratic expression of the same function with respect to space variables. For the resulting integrodifferential equation with quadratic nonlinearity, the Cauchy problem with initial data continuous and bounded on the positive semiaxis

Synthesis of Numerical Methods for Pareto Set Approximation Based on a Universal Procedure Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200512
Ya. I. RabinovichAbstract A universal computational procedure is used to construct numerical methods for Pareto set approximation. The numerical methods are developed relying on the assumptions necessary for proving the convergence of the universal procedure to the Pareto set.

On the Relation between the Properties of a Degenerate LinearQuadratic Control Problem and the Euler–Poisson Equation Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200512
V. F. Chistyakov, E. V. Chistyakova, Ta Zui FuongAbstract A quadratic functional with linear constraints in the form of differential equations with identically degenerate matrices multiplying the derivative of the state vector function is considered. The structure of the general solutions of such systems and some of their properties are discussed. On this basis, the conditions for the nonnegativity of the objective functional and small deviation

Displacement of Viscous Fluids in a Set of Parallel Pipes Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200512
G. V. Monakov, S. B. Tikhomirov, A. A. YakovlevAbstract The process of pumping water in a formation filled with a more viscous fluid is considered using the simplest model of the interwell space described by a set of parallel pipes. The fluids are assumed to be immiscible with a sharp interface in each pipe. The main task is to recover the parameters of the interwell space from a given displacement characteristic, namely, displacement data for

New Technique for Formulation of Domain Decomposition Algorithms Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200512
V. I. AgoshkovAbstract A new technique is proposed for constructing domain decomposition algorithms based on optimal control theory, the theory of inverse and illposed problems, application of adjoint equations, and modern iterative processes. The technique applies to a broad class of problems in mathematical physics (including ones with nonsymmetric operators, convectiondominant operators, etc.).

Explicit OneStep Numerical Method with the Strong Convergence Order of 2.5 for Ito Stochastic Differential Equations with a MultiDimensional Nonadditive Noise Based on the Taylor–Stratonovich Expansion Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200512
D. F. KuznetsovAbstract A strongly converging method of order 2.5 for Ito stochastic differential equations with multidimensional nonadditive noise based on the unified Taylor–Stratonovich expansion is proposed. The focus is on the approaches and methods of mean square approximation of iterated Stratonovich stochastic integrals of multiplicities 1–5 the numerical simulation of which is the main difficulty in the

Asymptotically Stable Periodic Solutions in One Problem of Atmospheric Diffusion of Impurities: Asymptotics, Existence, and Uniqueness Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200512
M. A. Davydova, A. L. NechaevaAbstract The basis of this work is the use of modern methods of asymptotic analysis in reaction–diffusion–advection problems in order to describe the classical boundarylayer periodic solution of one singularly perturbed problem for the nonlinear diffusion–advection equation. An asymptotic approximation of an arbitrary order of such a solution is constructed, and the formal construction is justified

Numerical Continuation Method for Nonlinear System of Scalar and Functional Equations Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200512
G. V. Paradezhenko, N. B. Melnikov, B. I. ReserAbstract We propose a numerical continuation method for a nonlinear system that consists of scalar and functional equations. At each parameter step, we solve the system by a modified Gauss–Seidel method. An advantage of this method is that the system is divided into two parts and each part is solved by a suitable numerical method with a desired precision. We solve the functional equations selfconsistently

Issues of Stability and Uniqueness of Stochastic Matrix Factorization Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200512
R. Yu. Derbanosov, I. A. IrkhinAbstract Two closely related problems—stability of the solution to the topic modeling problem and uniqueness of the stochastic matrix factorization are considered. A theorem describing an analytical method for finding out if the stability of the solution to a given stochastic matrix factorization problem is formulated and proved. The practical usefulness of this theorem is investigated by applying

Propagation of Electromagnetic Waves in an Open Planar Dielectric Waveguide Filled with a Nonlinear Medium II: TM Waves Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200512
D. V. ValovikAbstract A nonlinear eigenvalue problem on an interval is considered. The nonlinearity in the equation is specified by a nonnegative monotonically increasing function, and the boundary conditions nonlinearly depend both on the soughtfor functions and on the spectral parameter. The discrete eigenvalues are defined using an additional (local) condition at one end of the interval. This problem describes

Interface Capturing Method Based on the Cahn–Hilliard Equation for TwoPhase Flows Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200512
I. S. Menshov, C. ZhangAbstract A numerical method for flows of heterogeneous twophase compressible media is considered. The main problem in the construction of such a method is to find the interface between the components with different physical and mechanical properties. An efficient method for solving this problem that gives a good spatial resolution of the interfaces is proposed. This method is based on the use of the

Application of the Energy Conservation Law in the Cold Plasma Model Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200512
A. A. Frolov, E. V. ChizhonkovAbstract For the twofluid hydrodynamic cold plasma model, differential relations characterizing the energy conservation law are derived. The case when the motion of the heavier ions can be neglected as compared with the electrons and the situations with and without allowance for the relativistic factor in the electron dynamics are considered separately. For the problem of free plasma oscillations

Generalized Spline Interpolation of Functions with Large Gradients in Boundary Layers Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200512
I. A. Blatov, A. I. Zadorin, E. V. KitaevaAbstract The spline interpolation of functions of one variable with large gradients in boundary layers is studied. It is well known that applying polynomial splines to interpolate functions of this kind leads to significant errors when the small parameter is comparable with the grid step size. A generalized spline that is an analogue of a cubic spline is constructed. The spline is exact on the component

Stochastic Model of Heat Transfer in the Atmospheric Surface Layer Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200512
V. G. Zadorozhniy, V. S. Nozhkin, M. E. Semenov, I. I. Ul’shinAbstract A new stochastic model of heat transfer in the atmospheric surface layer is proposed. The model is based on the experimentally confirmed fact that the horizontal wind velocity can be treated as a random process. Accordingly, the model is formalized using a differential equation with random coefficients. Explicit formulas for the expectation and the second moment function of the solution to

The Problem of Identifying the Model of Substitution of Production Factors Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200512
E. G. MolchanovAbstract The generalized Houthakker–Johansen model that makes it possible to identify the substitution of production factors on the basis of the available Russian statistical data is studied. Combinatorial structures related to the problem of elasticity of production factor substitution at the microlevel are investigated. A necessary and a sufficient conditions for the solvability of the moment problem

Decomposition Implementation of Horner’s Scheme for Calculating the Values of Multidimentional Polynomials Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200417
A. P. Afanas’ev, S. M. DzyubaAbstract The paper presents a decomposition implementation of Horner’s scheme for calculating the values of multidimensional polynomials, which reduces the problem to calculating a sequence of values of onedimensional polynomials according to Horner’s scheme. The possibility of using this scheme in a distributed computer environment is studied. The operation of the scheme is exemplified by the problem

Analysis of Cluster Damages in Network Systems Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200417
Yu. E. Malashenko, I. A. Nazarova, N. M. NovikovaAbstract Changes in the functional characteristics of a multicommodity network with cluster architecture of the logical links depending on damages of edges of its physical topology graph are studied. The concept of a cluster damage is defined as a damage that separates at least one vertex from its sinks. The analysis is carried out on the class of minimum cluster damages. The stability of each cluster

Locally Polynomial Method for Solving Systems of Linear Inequalities Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200417
Yu. G. Evtushenko, A. A. Tret’yakovAbstract A numerical method combining a gradient technique with the projection onto a linear manifold is proposed for solving systems of linear inequalities. It is shown that the method converges in a finite number of iterations and its running time is estimated as a polynomial in the space dimension and the number of inequalities in the system.