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Erratum to: On Solutions of Elliptic Systems with a Jump at the Boundary Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20210104
A. O. BagapshAn Erratum to this paper has been published: https://doi.org/10.1134/S0965542520300016

Difference Scheme for the Numerical Solution of the Burgers Equation Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20210104
V. V. Markov, V. N. UtesinovAbstract A secondorder accurate finitedifference scheme based on existing methods is proposed for the numerical solution of the onedimensional Burgers equation. A stability condition is given under which the integration time step does not depend on the value of the viscous term. The numerical results produced by the scheme are compared with the exact solution of the Burgers equation.

Passage through Limiting Singular Points by Applying the Method of Solution Continuation with Respect to a Parameter in Inelastic Deformation Problems Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20210104
E. B. Kuznetsov, S. S. LeonovAbstract Numerical methods are developed for solving the Cauchy problem for systems of ordinary differential equations with a single limiting singular point lying on the right boundary of the considered range of the argument. Such initial value problems arise in a variety of areas, such as inelastic deformation of metal structures at various temperatures and stresses under creep conditions, the computation

Computation of Periodic Solutions to Pendulum Type Systems with a Small Parameter Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20210104
V. P. VarinAbstract Periodic solutions of pendulumtype ODE systems are considered. Finding such solutions is a classical problem in mechanics. Numerous methods are available for computing periodic solutions, and these methods have existed as long as the problems themselves. However, they were designed for manual calculation, and attempts to program them in computer algebra systems (CAS) are sometimes ineffective

Numerical Comparison of the Generalized Maxwell and Cercignani–Lampis Models Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20210104
A. A. FrolovaAbstract An anisotropic gas–surface interaction model is examined for its possible use as a boundary condition in solving a kinetic equation. The surface aerodynamic coefficients and the temperatures obtained by applying a twoparameter anisotropic reflection model and the Cercignani–Lampis boundary condition for external flow problems with various Knudsen numbers and accommodation coefficients are

Analytical Solution for the Cavitating Flow over a Wedge. I Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20210104
V. I. Vlasov, S. L. SkorokhodovAbstract The solution to the problem of cavitating flow of an ideal fluid over a wedge is represented in explicit form in terms of the Gauss and Appell hypergeometric functions for a number of classical cavity closure models. A numerical implementation of the solution is described in detail. Asymptotic representations of the drag coefficient \({{{\mathbf{C}}}_{x}}\) and the cavity sizes as the cavitation

Problem of Minimizing a Sum of Differences of Weighted Convolutions Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20210104
A. V. Kel’manov, L. V. Mikhailova, P. S. Ruzankin, S. A. KhamidullinAbstract A previously unstudied optimization problem concerning the summation of elements of numerical sequences \(Y\) and \(U\) of respective lengths \(N\) and \(q \leqslant N\) is considered. The task is to minimize the sum of differences between weighted convolutions of sequences of variable length (of at least \(q\)). In each difference, the minuend is a nonweighted autoconvolution of the sequence

Numerical Solution of a Stationary Filtration Problem of Viscous Fluid in a Piecewise Homogeneous Porous Medium by Applying the Boundary Integral Equation Method Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20210104
A. V. Setukha, R. M. TretyakovaAbstract A numerical method based on boundary integral equations is constructed for simulating threedimensional stationary filtration flow through a homogeneous porous medium with homogeneous inclusions. The flow is simulated taking into account the viscosity of the fluid. Boundary integral equations are written on the outer boundary of the flow region and on the boundary surfaces of the inclusions

Stable Method for Optical Monitoring the Deposition of Multilayer Optical Coatings Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20210104
I. V. Kochikov, Yu. S. Lagutin, A. A. Lagutina, D. V. Lukyanenko, A. V. Tikhonravov, A. G. YagolaAbstract For optical monitoring of layer thickness in the deposition of multilayer optical coatings, a stable method is proposed that completely eliminates the cumulative effect of errors in the thicknesses of deposited layers. The considered monitoring method relies on a nonlocal algorithm for analyzing data measured in the course of coating deposition monitoring. Computer simulation of coating deposition

Generalized Solutions of Quasilinear Elliptic DifferentialDifference Equations Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20210104
O. V. SolonukhaAbstract A Dirichlet problem for a functionaldifferential equation the operator of which is represented by the product of a quasilinear differential operator and a linear shift operator is considered. The nonlinear operator has differentiable coefficients. A sufficient condition for the strong ellipticity of the differentialdifference operator is proposed. For a Dirichlet problem with an operator

Modification of a Projection Method for Analysis of Radiation of a Radial Dipole in the Presence of an Inhomogeneous Body of Revolution Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20210104
E. I. Semernya, S. P. SkobelevAbstract The problem of radiation of a radial electric dipole located on the axis of rotation of an axisymmetric body consisting of a homogeneous dielectric sphere and an external inhomogeneous dielectric layer is considered. The new numerical algorithm developed to solve the problem is based on a projection method that includes the projection of fields to transverse spherical harmonics in combination

Projector Approach to the Butuzov–Nefedov Algorithm for Asymptotic Solution of a Class of Singularly Perturbed Problems in a Critical Case Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20210104
G. A. Kurina, N. T. HoaiAbstract Under some conditions, an asymptotic solution containing boundary functions of two types was constructed by V.F. Butuzov and N.N. Nefedov for initial value problems for differential equations involving the second power of a small parameter multiplying the derivative with a righthand side consisting of a singular matrix \(A(t)\) times the unknown function (as a linear part of the equation)

Building ZPermuted Matrices in the QTT Format Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20210104
L. B. Markeeva, I. V. TsybulinAbstract The paper presents a method for building matrices in the QTT format, the columns and rows of which are reordered in a special way, by zpermutation. To obtain a matrix in this permutation, a new operation in the QTT (Quantized Tensor Train) format, zkron, is introduced. This reordering allows one to reduce the QTT ranks of the approximation of the stiffness matrix, which makes it possible

Accelerated Methods for SaddlePoint Problem Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201208
M. S. Alkousa, A. V. Gasnikov, D. M. Dvinskikh, D. A. Kovalev, F. S. StonyakinAbstract Recently, it has been shown how, on the basis of the usual accelerated gradient method for solving problems of smooth convex optimization, accelerated methods for more complex problems (with a structure) and problems that are solved using various local information about the behavior of a function (stochastic gradient, Hessian, etc.) can be obtained. The term “accelerated methods” here means

On Regularity of Weak Solutions to a Generalized Voigt Model of Viscoelasticity Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201208
V. G. Zvyagin, V. P. OrlovAbstract The existence and uniqueness of a strong solution to the initialboundary value problem for a system of fluid dynamics equations that is a fractional analogue of the Voigt viscoelasticity model in the plane case are established. The rheological equation of this model involves fractional derivatives.

Biharmonic Obstacle Problem: Guaranteed and Computable Error Bounds for Approximate Solutions Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201208
D. E. Apushkinskaya, S. I. RepinAbstract The paper is concerned with an elliptic variational inequality associated with a free boundary obstacle problem for the biharmonic operator. We study the bounds of the difference between the exact solution (minimizer) of the corresponding variational problem and any function (approximation) from the energy class satisfying the prescribed boundary conditions and the restrictions stipulated

Numerical Study of a Singularly Perturbed Two Parameter Problems on a Modified Bakhvalov Mesh Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201208
P. Pramod Chakravarthy, Meenakshi ShivhareAbstract In this article, we consider a two parameter singular perturbation problem (TPSPP) and the numerical solution is obtained by using tension spline method on a layer adapted Bakhvalov type mesh. The method is analyzed for convergence. Numerical results are presented to support the theory.

Mechanism of Locomotion of Synthetic Nanomotors in a Viscous Fluid Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201208
S. I. Martynov, L. Yu. TkachAbstract A mechanism of nanomotor locomotion in a surrounding viscous fluid containing charged particles is considered. In contrast to a mechanism proposed in the literature, according to which nanomotor locomotion is induced by a concentration gradient of certain type particles produced by asymmetric chemical or electrochemical reactions occurring on the nanomotor surface, we hypothesize that nanomotor

Unreliability of Available Pseudorandom Number Generators Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201208
A. A. Belov, N. N. Kalitkin, M. A. TintulAbstract The problem of generating sequences of uniformly distributed pseudorandom numbers is considered. A simple visual test for estimating the randomness of numbers in a sequence is used. The test shows that the most popular modern random number generators, such as the Mersenne Twister, linear congruential sequence, and others, yield unsatisfactory results. Accordingly, the generation of good generators

On the Influence of the Beta Effect on the Spectral Characteristics of Unstable Perturbations of Ocean Currents Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201208
S. L. Skorokhodov, N. P. KuzminaAbstract Based on the equation for potential vorticity in the quasigeostrophic approximation, an analysis of stable and unstable perturbations of ocean currents of a finite transverse scale with a vertical linear velocity profile (Couettetype flows) is presented. The model takes into account the influence of vertical diffusion of buoyancy, friction, and the beta effect (the change in the Coriolis

Variational Method for Determining the ComplexValued Coefficients of a Nonlinear Nonstationary SchrödingerType Equation Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201208
M. A. MusaevaAbstract This study is devoted to variational methods for solving the problem of simultaneous determination of the unknown complexvalued coefficients multiplying the lower and nonlinear terms of a nonstationary Schrödingertype equation generalizing the wellknown quantum mechanical Schrödinger equation. The sought coefficient of the lower term is a complexvalued quantum potential. Problems of this

Computation of Asymptotic Spectral Distributions for Sequences of Grid Operators Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201208
S. V. Morozov, S. SerraCapizzano, E. E. TyrtyshnikovAbstract The asymptotic spectral properties of matrices of grid operators on polygonal domains in the plane are studied in the case of refining triangular grids. Methods available for analyzing spectral distributions are largely based on tool of the theory of generalized locally Toeplitz sequences (GLT theory). In this paper, we show that the matrices of grid operators on nonrectangular domains do

Asymptotics of the Riemann–Hilbert Problem for a Magnetic Reconnection Model in Plasma Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201208
S. I. Bezrodnykh, V. I. VlasovAbstract For the Riemann–Hilbert problem in a singularly deformed domain, an asymptotic expansion is found that corresponds to the limit transition from Somov’s magnetic reconnection model to Syrovatskii’s one as the relative shock front length \(\varrho \) tends to zero. It is shown that this passage to the limit corresponding to \(\varrho \to 0\) is performed with the preservation of the reverse

Recovery of Boundary Functions on External and Internal Open Boundaries in an Open Sea Hydrodynamic Problem Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201208
V. I. Agoshkov, N. R. Lezina, T. O. SheloputAbstract The inverse problem of recovering boundary functions on external and internal open boundaries for an open sea hydrodynamic model based on the linearized shallow water equations is considered. The external open boundary is meant as the boundary separating the considered water area from the world ocean. The internal open boundary is introduced to use the domain decomposition method. The inverse

A Note on a Posteriori Error Bounds for Numerical Solutions of Elliptic Equations with a Piecewise Constant Reaction Coefficient Having Large Jumps Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201208
V. G. KorneevAbstract We have derived guaranteed, robust, and fully computable a posteriori error bounds for approximate solutions of the equation \(\Delta \Delta u + {{\Bbbk }^{2}}u = f\), where the coefficient \(\Bbbk \geqslant 0\) is a constant in each subdomain (finite element) and chaotically varies between subdomains in a sufficiently wide range. For finite element solutions, these bounds are robust with

A Hybrid Method for the Computation of a Rarefied Gas Jet Efflux through a Very Long Channel into Vacuum Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201208
V. A. Titarev, E. M. ShakhovAbstract On the basis of the kinetic model, the steady efflux of monatomic gas from a high pressure camera (the Knudsen number \({\text{Kn}} \ll 1\)) through a long channel between two parallel plates into a vacuum camera under a constant temperature on the bounding surfaces is studied. Using asymptotic estimates for relatively long channels, the flow domain is divided into three subdomains: (1) a

Mathematical Modeling of the Wuhan COVID2019 Epidemic and Inverse Problems Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201208
S. I. Kabanikhin, O. I. KrivorotkoAbstract Mathematical models for transmission dynamics of the novel COVID2019 coronavirus, an outbreak of which began in December, 2019, in Wuhan are considered. To control the epidemiological situation, it is necessary to develop corresponding mathematical models. Mathematical models of COVID2019 spread described by systems of nonlinear ordinary differential equations (ODEs) are overviewed. Some

Convergence of Hölder Projections to Chebyshev Projections Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201208
V. I. Zorkal’tsevAbstract The problem of finding a point of a linear manifold with a minimal weighted Chebyshev norm is considered. In particular, to such a problem, the Chebyshev approximation is reduced. An algorithm that always produces a unique solution to this problem is presented. The algorithm consists in finding relatively internal points of optimal solutions of a finite sequence of linear programming problems

Sensitivity of the Euler–Poinsot Tensor Values to the Choice of the Body Surface Triangulation Mesh Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201122
A. A. Burov, V. I. NikonovAbstract The inertial characteristics of celestial bodies can be calculated using their triangle partitions based on photometric observations. Such partitions can be refined along with the accumulation of necessary information. In this regard, the question arises to what extent the approximations of the inertial characteristics of celestial bodies, in particular, the approximations of the components

Truncated Series and Formal ExponentialLogarithmic Solutions of Linear Ordinary Differential Equations Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201122
S. A. Abramov, A. A. Ryabenko, D. E. KhmelnovAbstract The approach we used earlier to construct Laurent and regular solutions enables one, in combination with the wellknown Newton polygon algorithm, to find formal exponentiallogarithmic solutions of linear ordinary differential equations the coefficients of which have the form of truncated power series. (Thus, only incomplete information about the original equation is available.) The series

Stochastic Processes on the Group of Orthogonal Matrices and Evolution Equations Describing Them Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201122
K. Yu. Zamana, V. Zh. Sakbaev, O. G. SmolyanovAbstract Stochastic processes that take values in the group of orthogonal transformations of a finitedimensional Euclidean space and are noncommutative analogues of processes with independent increments are considered. Such processes are defined as limits of noncommutative analogues of random walks in the group of orthogonal transformations. These random walks are compositions of independent random

Computation of Eigenfrequencies of an Acoustic Medium in a Prolate Spheroid by a Modified Abramov Method Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201122
T. V. LevitinaAbstract The method presented and studied in [1, 2] for solving selfadjoint multiparameter spectral problems for weakly coupled systems of ordinary differential equations is based on marching with respect to a parameter introduced into the problem. Although the method is formally applicable to systems of ordinary differential equations with singularities, its direct use for the numerical solution

Dirichlet Problem for a Generalized Cauchy–Riemann Equation with a Supersingular Point on a HalfPlane Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201122
I. N. Dorofeeva, A. B. RasulovAbstract For equations with a Cauchy–Riemann operator involving a strong point singularity in the lower coefficient on a halfplane, an integral representation of the solution is obtained in the class of bounded functions and a Dirichlettype problem is studied. The calculation of the Vekua–Pompeiu integral is examined in the case when the density of the integral has strong singularities in a set of

Best Recovery of the Solution of the Dirichlet Problem in a HalfSpace from Inaccurate Data Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201122
E. V. Abramova, G. G. MagarilIl’yaev, E. O. SivkovaAbstract A family of linear optimal methods for reconstructing the solution of the Dirichlet problem on a hyperplane from information about its approximate measurements on a finite number of other hyperplanes is constructed. In this case, optimal methods do not use all the available information, but only information about the measurements of the solution on at most two planes.

RiskFree Investments and Their Comparison with Simple Risky Strategies in Pension Insurance Model: Solving Singular Problems for IntegroDifferential Equations Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201122
T. A. Belkina, N. B. Konyukhova, B. V. SlavkoAbstract A collective pension insurance (life annuity) model is investigated in the case of riskfree investments, i.e., when the whole surplus of an insurance company at each time is invested in riskfree asset (bank account). This strategy is compared with previously studied simple risky investment strategies, according to which, irrespective of the surplus of an insurance company, a constant positive

On Numerical Solution of One Class of IntegroDifferential Equations in a Special Case Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201122
N. S. GabbasovAbstract A complete theory of solvability of a linear integrodifferential equation with a coefficient having powerlaw zeros is developed. For its approximate solution in the space of generalized functions, special generalized versions of the collocation method based on the use of standard polynomials and cubic splines of minimal defect are proposed and justified. Optimality in the order of accuracy

Stationary States in a Model of Position Selection by Individuals Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201122
A. P. Petrov, O. G. PronchevaAbstract A model of position selection by individuals in the propaganda battle of two parties is considered. The position selection is based on a neurological decisionmaking model the input of which is the information stimuli arriving to the individual from the opposing parties and which produces as its output the support of one of these parties. In this version of the model, assortativity and the

Mathematical Simulation of Satellite Motion with an Aerodynamic Attitude Control System Influenced by Active Damping Torques Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201122
S. A. Gutnik, V. A. SarychevAbstract The dynamics of a satellite moving in a central Newtonian force field in a circular orbit under the influence of aerodynamic and active damping torques depending on projections of the satellite’s angular velocity is studied. A method for determining all equilibrium positions (equilibrium orientations) of the satellite in the orbital coordinate system given the values of aerodynamic torque

Choice of FiniteDifference Schemes in Solving Coefficient Inverse Problems Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201122
A. F. Albu, Yu. G. Evtushenko, V. I. ZubovAbstract Various choices of a finitedifference scheme for approximating the heat diffusion equation in solving a threedimensional coefficient inverse problem were studied. A comparative analysis was conducted for several alternating direction schemes, such as locally onedimensional, Douglas–Rachford, and Peaceman–Rachford schemes, as applied to nonlinear problems for the threedimensional heat equation

Singularly Perturbed Cauchy–Riemann Equation with a Singularity in the Lower Coefficient Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201122
A. B. Rasulov, Yu. S. FedorovAbstract The Lomov regularization method is generalized to a singularly perturbed Cauchy–Riemann equation with a singularity in the lower coefficient.

A Heuristic Rational Algorithm for Checking the Congruence of Normal Matrices Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201122
Kh. D. Ikramov, A. M. NazariAbstract A finite algorithm that uses arithmetic operations only is said to be rational. There exist rational methods for checking the congruence of a pair of Hermitian matrices or a pair of unitary ones. We propose a rational algorithm for checking the congruence of general normal matrices.

Simulation of the Interaction of Oppositely Directed Particle Flows Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201122
S. Ya. Stepanov, T. V. SalnikovaAbstract A mathematical model of the early stage of the formation of interstellar clouds resulting from the interaction of oppositely directed cosmic particle flows and evolution of the clouds into planetary systems is proposed. An important role in the evolution is played by mechanical energy dissipation caused mainly by particle collisions. The simulation is based on the classical nbody problem

Testing a New Conservative Method for Solving the Cauchy Problem for Hamiltonian Systems on Test Problems Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201101
P. A. Aleksandrov, G. G. EleninAbstract A new numerical method for solving the Cauchy problem for Hamiltonian systems is tested in detail as applied to two benchmark problems: the onedimensional motion of a point particle in a cubic potential field and the Kepler problem. The global properties of the resulting approximate solutions, such as symplecticity, time reversibility, total energy conservation, and the accuracy of numerical

Boundary Conditions for Modeling the Impact of Wheels on Railway Track Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201101
A. A. Kozhemyachenko, I. B. Petrov, A. V. Favorskaya, N. I. KhokhlovAbstract The distribution of the dynamic load on railroad track caused by a moving heavy train is numerically simulated. The track is represented as a multilayered linear elastic medium. A complete system of equations describing the state of a linear elastic body and a system of continuum mechanics equations are solved. The gridcharacteristic method is used, which ensures the formulation of correct

A New View of Some Fundamental Results in Optimization Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201101
Yu. G. Evtushenko, A. A. Tret’yakovAbstract Some fundamental optimization results are proved in new ways, which are not traditional and provide a new view of wellknown results. Constructions of \(p\)regularity theory are used to justify the facts under consideration, and the 2factor method is applied to solve singular problems.

Dynamics of an Elastic Punch on an Elastic HalfPlane with Crack Formation Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201101
L. A. Alexeyeva, T. B. Duishenaliyev, B. T. SarsenovAbstract The dynamics of buildings and structures in an earthquake zone is studied relying on a model boundary value problem describing the dynamics of an elastic punch on an elastic halfplane under diffraction and refraction of waves generated by stress release on a crack. The problem is solved by applying an explicit difference scheme constructed using the method of bicharacteristics combined with

Numerical Method for Solving a System of Kinetic Equations Describing the Behavior of a Nonideal Gas Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201101
M. V. Abgaryan, A. M. Bishaev, V. A. RykovAbstract A previously constructed kinetic model for describing the behavior of a nonideal gas is investigated. The dimensionless parameters determining when the nonideal nature of the gas has to be taken into account are estimated in more detail. It is found that the collision integral for bound particles can be integrated over the velocity space, which significantly simplifies the original system

Multicriteria Competitive Games as Models in Operations Research Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201101
E. M. Kreines, N. M. Novikova, I. I. PospelovaAbstract The problem of a priori estimation of the result of a mulicriteria twoperson competitive game is considered in the framework of operations research. Various aspects of decision making in such games are discussed. Relations between the values of a vector best guaranteed result (BGR) for both players are obtained. The difference of the mulicriteria antagonistic game considered as a model of

Total Approximation Method for an Equation Describing Droplet Breakup and Freezing in Convective Clouds Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201101
B. A. Ashabokov, A. Kh. Khibiev, M. Kh. ShkhanukovLafishevAbstract A locally onedimensional scheme for a general parabolic equation in a \(p\)dimensional parallelepiped is considered. A special nonlocal integral source is added to the considered equation to describe droplet breakup and freezing in convective clouds. An a priori estimate for the solution of the locally onedimensional scheme is obtained, and its convergence is proved.

On a Periodic Inner Layer in the Reaction–Diffusion Problem with a Modular Cubic Source Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201101
N. N. Nefedov, E. I. Nikulin, A. O. OrlovAbstract The article studies a singularly perturbed periodic problem for the parabolic reaction–diffusion equation in the case of a discontinuous source: a nonlinearity describing the reaction (interaction). The case of the existence of an inner transition layer under conditions of an unbalanced and a balanced reaction is considered. An asymptotic approximation is constructed, and the asymptotic Lyapunov

On Solutions of Elliptic Systems with a Jump at the Boundary Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201101
A. O. BagapshAbstract The Dirichlet problem for a strongly elliptic system of the second order with constant coefficients in the domain with a piecewise smooth boundary and piecewise continuous boundary data is considered. The behavior near the jump point of the boundary function is shown.

Determination of Compactly Supported Sources for the OneDimensional Heat Equation Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201101
V. V. Solov’evAbstract The inverse problem of determining a source in the onedimensional heat equation in the case of a Dirichlet boundary value problem is investigated. The trace of the solution of the direct problem on straightline segments inside the domain at the final time is specified as overdetermination (i.e., additional information on the solution of the direct problem). A Fredholm alternative theorem

AnalyticalNumerical Study of FiniteTime Blowup of the Solution to the InitialBoundary Value Problem for the Nonlinear Klein–Gordon Equation Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201101
M. O. Korpusov, A. N. Levashov, D. V. LukyanenkoAbstract An analyticalnumerical approach is used to study the finitetime blowup of the solution to the initial boundaryvalue problem for the nonlinear Klein–Gordon equation. An analytical analysis yields an upper estimate for the blowup time of the solution with an arbitrary positive initial energy. With the use of this a priori information, the blowup process is numerically analyzed in more

Modeling of the Turbulent Poiseuille–Couette Flow in a Flat Channel by Asymptotic Methods Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201101
V. B. ZametaevAbstract Developed turbulent flow of a viscous incompressible fluid in a channel of small width at high Reynolds numbers is considered. The instantaneous flow velocity is represented as the sum of a stationary component and small perturbations, which are generally different from the traditional averaged velocity and fluctuations. The study is restricted to the search for and consideration of stationary

Gradient Projection Method on Matrix Manifolds Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201101
M. V. BalashovAbstract The minimization of a function with a Lipschitz continuous gradient on a proximally smooth subset of a finitedimensional Euclidean space is considered. Under the restricted secant inequality, the gradient projection method as applied to the problem converges linearly. In certain cases, the linear convergence of the gradient projection method is proved for the real Stiefel or Grassmann manifolds

Analytical Study on the Generalized FifthOrder Kaup–Kupershmidt Equation from the Shallow Water Wave Comput. Math. Math. Phys. (IF 0.565) Pub Date : 20201101
Pan Wang, JianRong Yang, Li Chen, ShengXin Li, FengHua QiAbstract In this paper, the generalized fifthorder Kaup–Kupershmidt (KK) equation from the shallow water wave, have been investigated. With the help of bilinear method and auxiliary function, the multisoliton solutions of the generalized fifthorder KK equation have been obtained, and those solutions have not been given before. From the analytical view, the interactions of the solitons have been

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