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Efficient Asymptotics in Problems on the Propagation of Waves Generated by Localized Sources in Linear Multidimensional Inhomogeneous and Dispersive Media Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201007
S. Yu. Dobrokhotov, V. E. NazaikinskiiAbstract The Cauchy problem with localized initial conditions is considered for a large class of evolution equations that includes the Schrödinger and Dirac equations, Maxwell equations, linearized fluid dynamics equations, equations of the linear theory of surface water waves, equations of elasticity theory, acoustics equations, and many others. A general approach to the construction of efficient

Harnack Inequality for the Elliptic p ( x )Laplacian with a ThreePhase Exponent p ( x ) Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201007
Yu. A. Alkhutov, M. D. SurnachevAbstract For an elliptic \(p(x)\)Laplacian with a piecewise constant threephase exponent \(p\) in the plane with three phases joining at a point, a Harnack inequality is proved and the Hölder continuity of the solution is established.

Darwin Approximation for the System of Maxwell’s Equations in Inhomogeneous Conducting Media Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201007
A. V. Kalinin, A. A. TyukhtinaAbstract A quasistationary Darwin approximation for the system of Maxwell’s equations in inhomogeneous conducting media is studied. An existence and uniqueness theorem for the initialboundary value problem for the resulting system of differential equations is proved. Estimates of the proximity between the solutions of the quasistationary problem under consideration and the corresponding nonstationary

Variational Method for Computing Ray Trajectories and Fronts of Tsunami Waves Generated by a Localized Source Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201007
S. Yu. Dobrokhotov, M. V. Klimenko, I. A. Nosikov, A. A. TolchennikovAbstract A variational approach for solving the boundary value problem of computing ray trajectories and fronts of ocean waves is presented. The solution method is based on Fermat’s principle (of stationary time). A distinctive feature of the proposed approach is that the Fermat functional is optimized directly without solving the Euler–Lagrange equation; moreover, the locations of the wave source

Identification Problem for TelegraphParabolic Equations Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201007
A. Ashyralyev, M. Ashyraliyev, M. A. AshyralyyevaAbstract An identification problem for an equation of mixed telegraphparabolic type with an unknown parameter depending on spatial variables is considered. The unique solvability of this problem is proved, and stability inequalities for its solution are established. As applications, stability estimates are obtained for the solutions of four identification problems for telegraphparabolic equations

WellPosedness and Spectral Analysis of Integrodifferential Equations of Hereditary Mechanics Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201007
V. V. Vlasov, N. A. RautianAbstract The wellposedness of initial value problems for abstract integrodifferential equations with unbounded operator coefficients in Hilbert spaces is studied, and spectral analysis of the operator functions that are the symbols of these equations is performed. The equations under consideration are an abstract form of linear partial integrodifferential equations arising in viscoelasticity theory

Influence of the Second Delay on Local Dynamics Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201007
I. S. KashchenkoAbstract The local dynamics of singularly perturbed equations with two delays are studied in the case when both delays are asymptotically large and identical in the order of magnitude (proportional). Critical cases are identified, and all of them are shown to have an infinite dimension. To examine the behavior of solutions near the critical cases, special nonlinear equations—quasinormal forms—are

Nonexistence of SignChanging Solutions for Some Elliptic Inequalities in Bounded Domains Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201007
E. I. Galakhov, O. A. SalievaAbstract Nonlinear elliptic inequalities in bounded domains and systems of such inequalities involving terms depending differently on the positive and negative parts of the sought function are considered. Sufficient conditions for the nonexistence of nontrivial solutions to the inequalities and systems under study in corresponding functional classes are obtained.

Functional Differential Equations of Pointwise Type: Bifurcation Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201007
L. A. Beklaryan, A. L. BeklaryanAbstract The importance of functional differential equations of pointwise type is determined by the fact that their solutions are used to construct travelingwave solutions for induced infinitedimensional ordinary differential equations, and vice versa. Solutions of such equations exhibit bifurcation. A theorem on branching bifurcation is obtained for the solution to a linear homogeneous functional

Decay of Nonnegative Solutions of Singular Parabolic Equations with KPZNonlinearities Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201007
A. B. MuravnikAbstract The Cauchy problem for quasilinear parabolic equations with KPZnonlinearities is considered. It is proved that the behavior of the solution as \(t \to \infty \) can change substantially as compared with the homogeneous case if the equation involves zeroorder terms. More specifically, the solution decays at infinity irrespective of the behavior of the initial function and the rate and character

On One Integral Equation in the Theory of Transform Operators Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201007
S. M. SitnikAbstract Integral representations of solutions of one differential equation with singularities in the coefficients, containing the Bessel operator perturbed by some potential, are considered. The existence of integral representations of a certain type for such solutions is proved by the method of successive approximations using transform operators. Potentials with strong singularities at the origin

Dynamics of a Set of Quantum States Generated by a Nonlinear Liouville–von Neumann Equation Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201007
A. D. Grekhneva, V. Zh. SakbaevAbstract A model describing the dynamics of a set of quantum states generated by a nonlinear Schrödinger equation is studied. The relationship between the blowup of a solution with selffocusing and the transition from pure to mixed states of a quantum system was investigated in [1]. In this context, a natural question is concerned with the dynamics generated by the nonlinear Schrödinger equation

On Boundary Value Problems for an Improperly Elliptic Equation in a Circle Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201007
V. P. Burskii, E. V. LesinaAbstract The paper considers the solvability of the first, second, and third boundary value problems, as well as one problem with a directional derivative, in a bounded domain for a scalar improperly elliptic differential equation with complex coefficients. More detailed consideration is given to a model case in which the domain is a unit disk and the equation does not contain lowerorder terms. For

Parametrization of Solutions to the Emden–Fowler Equation and the Thomas–Fermi Model of Compressed Atoms Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201007
S. V. PikulinAbstract For the nonlinear Emden–Fowler equation, a singular Cauchy problem and singular twopoint boundary value problem on the halfline \(r \in [0, + \infty )\) and on an interval \(r \in [0,R]\) with a Dirichlet boundary condition at the origin and with a Robin boundary condition at the right endpoint of the interval are considered. For special parameter values, the given boundary value problem

Application of Supporting Integral Curves and Generalized Invariant Unbiased Estimation for the Study of a Multidimensional Dynamical System Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200809
Yu. G. BulychevAbstract The wellknown methods of supporting integral curves and generalized invariant unbiased estimation are used to find numericalanalytical representations of the solution to an equation describing a dynamical system and its measured output and to compute optimal values of continuous linear functionals (numerical characteristics) of measured parameters based on incorrect data involving both a

Numerical Modeling of Passive Scalar Transport in Shallow Water Based on the QuasiGasdynamic Approach Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200809
T. G. Elizarova, A. V. IvanovAbstract A new method for the numerical solution of the passive scalar transport equation in the framework of hydrodynamic equations in the shallow water approximation is described. The method is based on previously developed quasigasdynamic algorithms for numerical simulation of compressible gas flows. Smoothed equations are derived, and their difference approximations, including for flows with a

Asymptotic Expansion of Legendre Polynomials with Respect to the Index near x = 1: Generalization of the Mehler–Rayleigh Formula Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200809
L. A. Bakaleinikov, E. A. TroppAbstract An asymptotic expansion of the Legendre polynomials \({{P}_{n}}\left( x \right)\) in inverse powers of the index \(n\) in a neighborhood of \(x = 1\) is obtained. It is shown that the expansion coefficient of \({{n}^{{  k}}}\) is a linear combination of terms of the form \({{\rho }^{p}}{{J}_{p}}\left( \rho \right)\), where \(0 \leqslant p \leqslant k\). It is also shown that the first terms

Construction and Analysis of Explicit Adaptive OneStep Methods for Solving Stiff Problems Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200809
L. M. SkvortsovAbstract The paper considers the construction of adaptive methods based on the explicit Runge–Kutta stages. The coefficients of these methods are adjusted to the problem being solved, using componentwise estimates of the eigenvalues of the Jacobi matrix with the maximum absolute values. Such estimates can be easily obtained at the stages of the explicit method, which practically does not require additional

Nested Implicit Runge–Kutta Pairs of Gauss and Lobatto Types with Local and Global Error Controls for Stiff Ordinary Differential Equations Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200809
G. Yu. KulikovAbstract The problem of efficient global error estimation and control is studied in embedded nested implicit Runge–Kutta pairs of Gauss and Lobatto types as applied to stiff ordinary differential equations (ODEs). Stiff problems may arise in many areas of engineering, and their accurate numerical solution is an important issue of computational and applied mathematics. A cheap global error estimation

Equations Describing Waves in Tubes with Elastic Walls and Numerical Methods with Low Scheme Dissipation Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200809
I. B. BakholdinAbstract Equations for a tube with elastic waves (tube with controlled pressure, fluidfilled tube, and gasfilled tube) are considered. A full membrane model and the nonlinear theory of hyperelastic materials are used for describing the tube walls. The Riemann problem is solved, and its solutions confirm the theory of reversible discontinuity structures. Dispersion of short waves for such equations

Inviscid Instability of an Incompressible Boundary Layer on a Compliant Surface Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200809
I. V. SavenkovAbstract The instability of an incompressible boundary layer on a compliant plate with respect to inviscid perturbations is analyzed on the basis of tripledeck theory. It is shown that unstable inviscid perturbations persist only if the inertia of the plate is taken into account. It is found that an important role is played by the bending stiffness of the plate. Specifically, as it approaches a certain

Spectral Estimates for the FourthOrder Operator with Matrix Coefficients Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200809
D. M. PolyakovAbstract The fourthorder differential operator with matrix coefficients with the domain determined by quasiperiodic boundary conditions is considered. For this operator, the asymptotics of the arithmetic mean of the eigenvalues is found. Moreover, for various special cases, the asymptotics of the eigenvalues is also obtained. The spectral characteristics in the case of periodic and antiperiodic boundary

Quadrature Formulas of Gauss Type for a Sphere with Nodes Characterized by Regular Prism Symmetry Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200809
A. M. Voloshchenko, A. A. RusskovAbstract When the transport equation is solved by the discrete ordinate method, the problem arises of constructing quadrature formulas on a sphere characterized by the required accuracy and making it possible to use the quadrature nodes to approximate the transport equation in \(r,\;\vartheta ,\;z\) geometry, in which quadrature nodes are simultaneously used to approximate the derivative with respect

A Heuristic Adaptive Fast Gradient Method in Stochastic Optimization Problems Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200809
A. V. Ogal’tsov, A. I. TyurinAbstract A fast adaptive heuristic stochastic gradient descent method is proposed. It is shown that this algorithm has a higher convergence rate in practical problems than currently popular optimization methods. Furthermore, a justification of this method is given, and difficulties that prevent obtaining optimal estimates for the proposed algorithm are described.

Synthesis of Locally Lumped Controls for Membrane Stabilization with Optimization of Sensor and Vibration Suppressor Locations Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200809
K. R. Aidazade, V. A. HashimovAbstract An approach for synthesizing a control function for lumped sources in distributed feedback systems is proposed. The problem of membrane vibration suppression by point stabilizers is considered as an example. The parameters to be optimized in the problem are (1) the locations of the stabilizers, (2) the locations of the points of membrane state measurements, and (3) linear feedback parameters

Method for Experimental Data Processing Concerning Chemical Reaction Rates in LowAtomic Gases Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200809
A. A. Belov, N. N. KalitkinAbstract A new method for joint processing of experimental data from various laboratories based on their approximation by the generalized Arrhenius law is proposed. The method is based on the construction of a system of functions that are orthogonal on a given set of points with arbitrary weights. As a result, the confidence intervals of the approximation coefficients can be estimated and the number

Uniformly a posteriori Error Estimates for Regularizing Algorithms Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20200809
M. M. KokurinAbstract A modification for the definition of an a posteriori error estimate for a regularizing algorithm for solving an illposed problem is proposed. We introduce, analyze and illustrate by examples the concept of a uniformly a posteriori error estimate for a regularizing algorithm. A necessary and sufficient condition for the existence of a regularizing algorithm satisfying such an estimate is established

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