Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
ISSN (print): 0044-4669
Founders: Russian Academy of Sciences, Federal Research Center IU named after. A. A. Dorodnitsyna RAS
Editor-in-Chief: Evgeniy Evgenievich Tyrtyshnikov, Academician of the Russian Academy of Sciences, Doctor of Physics and Mathematics sciences, professor
Frequency / access: 12 issues per year / Subscription
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Media registration certificate: № 0110141 от 04.02.1993
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Vol 65, No 4 (2025)
General numerical methods
APPROXIMATION OF THE FUNCTION AND ITS DERIVATIVE RELATING TO THE HOLDER–LIPSCHITZ CLASS WITH THEIR FOURIER COEFFICIENTS FOR A HARMONICALLY MODULATED ARGUMENT
Abstract
The paper considers the proved theorems according to which any function and its derivative relating to the Holder–Lipschitz class α(G) can be approximated with any pre-set accuracy by a finite sum of the dependences of the Fourier coefficients for a harmonically modulated function argument.
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki. 2025;65(4):417–425
417–425
APPROXIMATION OF TABULATED FUNCTIONS: A MULTI-CRITERIA APPROACH. PART II
Abstract
The article continues the development of a new approach to evaluate approximation parameters, in which the distance of the approximating function from the given finite set of points is estimated by a vector criterion, its components are the modules of residuals at all points. The vector criterion is used to define the distance preference ratio, and the best approximation function is considered to be nondominant with respect to this ratio. Compared to the first article of the authors (“Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki”, 2022), which is devoted to parametric methods, the present article offers nonparametric methods for several preference relations, including the Pareto relation and the relation generated by the information about the equality of criteria. Computational problems are considered and the relations between the introduced approximating functions and classical ones are investigated. Calculated examples are provided.
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki. 2025;65(4):426–433
426–433
Partial Differential Equations
ALGORITHMS FOR LOCALIZATION OF SCATTERING INHOMOGENEITIES BASED ON INCOMPLETE MULTIPATH ULTRASOUND DATA
Abstract
The considered inverse problem for a nonstationary integro-differential equation for the highfrequency acoustic radiation transport which lies in determining the discontinuity surfaces of the volume scattering coefficient from the time-angular distribution of the flow density at a given point in threedimensional space. Numerical algorithms for solving the inverse problem based on the introduction of special indicator functions that explicitly indicate the location of the scattering coefficient discontinuity lines in a given plane are proposed. Monte Carlo methods allowed simulating the process of ultrasonic sounding in the marine environment, the effectiveness of the algorithms for localization of scattering inhomogeneities was demonstrated, and the effect of the initial data incompleteness on the quality of tomographic images was numerically analyzed.
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki. 2025;65(4):434–445
434–445
THE JACOBI-MAUPERTUIS PRINCIPLE AND FERMAT VARIATIONAL PRINCIPLE IN THE PROBLEM OF SHORT-WAVE ASYMPTOTICS IN THE SOLUTION OF THE HELMHOLTZ EQUATION WITH A LOCALIZED SOURCE
Abstract
The problem of short-wave asymptotics of the Helmholtz equation with a localized right-hand side in the form of a rapidly decreasing function is considered in the article. We present an algorithm for calculating rays using the variational method and the wave field applying the canonical Maslov operator method for given boundary conditions. This approach is used for model examples, including those with a logarithmic feature of the ray family. In addition, we consider applications of the variational method for calculating rays in the illuminated region and in the caustic shadow region.
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki. 2025;65(4):446–459
446–459
FIRST BOUNDARY VALUE PROBLEM FOR THE HEAT CONDUCTION EQUATION IN TIME-DEGENERATE DOMAINS
Abstract
We consider the first boundary value problem in a cone with a degeneracy of the domain at the initial moment of time for the heat equation. Own functions for the problem were found. Estimations of the Green’s function are obtained. For the problem with a zero boundary function, we establish unambiguous solvability in a certain class of functions that admits a definite growth when approaching the vertex of a cone. Similar results are obtained for the cone that degenerates at the final point in time. In addition, we consider the first boundary value problem in domains that are degenerate only in terms of variables.
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki. 2025;65(4):460–470
460–470
ON THE DESTRUCTION OF SOLUTIONS TO CAUCHY PROBLEMS FOR NONLINEAR FERRITE EQUATIONS IN (N + 1)–DIMENSIONAL CASE
Abstract
In this paper, we consider three Cauchy problems for (N + 1) dimensional nonlinear Sobolevtype equations arising in the theory of magnetic vibrations in ferrites. We obtain results on the existence and uniqueness of weak solutions to these problems that are local in time, as well as on the existence and uniqueness of weak solutions to these problems, and on destroying these solutions.
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki. 2025;65(4):471–493
471–493
GAPS IN THE SPECTRUM OF A PERIODIC FAMILY OF BODIES CONNECTED BY THIS ELASTIC RODS
Abstract
We investigate the low-frequency range of the spectrum of periodic spacial isotropic and homogeneous elastic waveguide composed from identical massive bodies which are connected by thin cylindrical rods. By means of the dimension reduction procedure for the rods and analysis of interaction of singular fields and rigid motions in the body we construct asymptotics of dependent on the Floquet variable eigenvalues of the model problem on the periodicity cell and found out size and position of spectral bands (wave passing zones) inside the low-frequency range as well as detect open spectral gaps (wave stopping zones). We also formulate open questions, in particular, about existence of open gaps in thу spectrum of analogous planar elastic waveguide.
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki. 2025;65(4):494–514
494–514
CHOOSING THE BROADBAND MONITORING ALGORITHM FOR THE DEPOSITION PROCESS OF OPTICAL COATINGS WITH ACCOUNTING FOR THE SELF-COMPENSATION EFFECT OF ERRORS
Abstract
Two algorithms for broadband optical monitoring of the deposition of optical coatings are considered: the first one is without solving the additional inverse problem for refining the thicknesses of already deposited layers, the second one is with its solution. It is shown that refinement of the thicknesses of already deposited layers reduces errors in the layer thicknesses, but does not always provide a more accurate implementation of the required spectral properties of the coating. It is demonstrated for the first time that when choosing a control algorithm, the presence of the error self-compensation effect should be taken into account.
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki. 2025;65(4):515–527
515–527
Mathematical physics
ICOMPACT SCHEMES ON LOCALLY ADAPTIVE CARTESIAN GRIDS FOR THE CONVECTION-DIFFUSION EQUATION
Abstract
High-precision bicompact schemes are considered for the multidimensional convection-diffusion equation with constant coefficients. A new implementation of these schemes on regular Cartesian grids is constructed on the basis of a single replacement of dependent variables and a simplified statement of boundary conditions. Unlike the earlier used implementation, it is a multidimensional running counter that allows you to interpolate the desired functions on the edges and faces of cells "on the fly that is, in the process of traversing the latter. Due to this property, the new implementation is generalized to hierarchical Cartesian meshes with local adaptive thickening depending on the solution. The results of testing the computational algorithm in wide ranges of the Courant number and the number of adaptation levels are presented, which demonstrate high third -order accuracy.
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki. 2025;65(4):528–547
528–547
NUMERICAL STUDY OF DRIFT-DISSIPATIVE INSTABILITY IN THE REGION OF EQUATORIAL PLASMA BUBBLES FOR DIFFERENT GEOPHYSICAL CONDITIONS
Abstract
In the paper, we study the dependences of the linear increment of drift-dissipative instability in the equatorial region of the Earth ionosphere on helio-geomagnetic conditions, ionospheric parameters, and characteristics of equatorial plasma bubbles, on the fronts of which small-scale plasma inhomogeneities can develop. In the works of both the authors of the article and numerous studies by other authors, a high degree of correlation of the F-scattering phenomenon with the presence of plasma bubbles in the equatorial F-region of the ionosphere has been revealed. The classical explanation of F-scattering is related to the appearance and development of small-scale inhomogeneities on the fronts of equatorial plasma bubbles. The time period favorable for the generation and development of equatorial plasma bubbles is from one to two hours. The study was carried out in the form of a series of computational experiments, using the original two–dimensional mathematical and numerical model of Rayleigh-Taylor instability development developed earlier by the authors. Numerical simulations were performed for geophysical conditions favorable for the development of equatorial plasma bubbles in the equatorial F-region of the Earth ionosphere. This work is a continuation of the authors’ research. In contrast to the previous works of the authors, this paper examines the features of the increment of drift-dissipative instability depending on a wide range of conditions and parameters of the low-latitude ionosphere.
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki. 2025;65(4):548–557
548–557
FINITE-DIFFERENCE SCHEME OF THE FIFTH ORDER BY SPACE WITH THE INCREASED ACCURACY IN AREAS OF SHOCK WAVES’ INFLUENCE
Abstract
A new finite-difference (NFD) scheme of the fifth order in space and the third order in time which preserves increased accuracy in the regions of shock wave influence is constructed. A comparative analysis of the NFD scheme accuracy with the RBM (Rusanov–Burstein–Mirin) and A-WENO (Alternative Weighted Essentially Non-Oscillatory) schemes is performed in the calculation of a special Cauchy problem with smooth periodic initial data for shallow water equations, in the exact solution of which shock waves arise inside the calculated region as a result of gradient catastrophes. It is shown that in smooth parts of the approximated solution, outside the regions of influence of shock waves, the NFD scheme is significantly more accurate than the third-order RBM scheme, and on sufficiently coarse numerical grids it is more accurate than the fifth-order A-WENO scheme in space and third-order in time; on smaller numerical grids, the NFD and A-WENO schemes have approximately the same accuracy in these parts of the calculated solution. In areas of impact of shock waves, where the RBM scheme becomes significantly more accurate than the A-WENO scheme, the NFD scheme has a higher accuracy than the RBM schema.
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki. 2025;65(4):558–573
558–573
Computer science
DYNAMIC SELF-ORGANIZATION IN NEURAL NETWORKS SYSTEMS
Abstract
The introduced concept of dynamic self-organization consists in the following. Suppose that there is a set of free (non-interacting) neurons, each of which is at rest or not capable of vibrational electrical activity at all. Then, being connected in a certain way in a network, these neurons can begin to generate electrical impulses. The feasibility of this phenomenon is illustrated by the example of one mathematical model, which is a certain nonlinear boundary value problem of hyperbolic type. A combination of analytical and numerical methods is used to study the attractors of the boundary value problem under consideration.
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki. 2025;65(4):574–589
574–589
DENTIFICATION OF SPLIT FACTORS IN PEDESTRIAN FLOWS MODELING
Abstract
The paper is devoted to mathematical modeling of indoor pedestrian flows. The model under consideration is an analogue of the CTM transport macromodel. The current work explores the possibility of identifying split factors that were previously considered a priori given. These coefficients denote the proportions in which a flow of people is divided when moving to other rooms from the current one. We propose an identification algorithm based on interval estimates of both forward and backward reachability sets. The algorithm is illustrated with a numerical example.
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki. 2025;65(4):590–602
590–602