Discrete and Continuous Models and Applied Computational Science

Editor-in-Chief: Yuriy P. Rybakov, Doctor of Science (Physics and Mathematics), Professor, Honored Scientist of Russia

ISSN: 2658-4670 (Print). ISSN: 2658-7149 (Online)

Founded in 1993. Publication frequency: quarterly.

Peer-Review: double blind. Publication language: English. 

APC: no article processing charge. Open Access: Open Access

PUBLISHER: Peoples’ Friendship University of Russia (RUDN University)

See the Journal History to get information on previous journal titles.

Indexation: Russian Index of Science Citation, VINITI RAS, DOAJ, Google Scholar, Ulrich's Periodicals Directory, WorldCat, Cyberleninka, East View, Dimensions, EBSCOhost, ResearchBib, Lens, Research4Life, JournalTOCs

 

Discrete and Continuous Models and Applied Computational Science was created in 2019 by renaming RUDN Journal of Mathematics, Information Sciences and Physics. RUDN Journal of Mathematics, Information Sciences and Physics was created in 2006 by combining the series "Physics", "Mathematics", "Applied Mathematics and Computer Science", "Applied Mathematics and Computer Mathematics".

Discussed issues affecting modern problems of physics, mathematical modeling, computer science. The widely discussed issues Teletraffic theory, queuing systems design, software and databases design and development.

Discussed problems in physics related to quantum theory, nuclear physics and elementary particle physics, astrophysics, statistical physics, the theory of gravity, plasma physics and the interaction of electromagnetic fields with matter, radio physics and electronics, nonlinear optics.

Journal has a high qualitative and quantitative indicators. The Editorial Board consists of well-known scientists of world renown, whose works are highly valued and are cited in the scientific community. Articles are indexed in the Russian and foreign databases. Each paper is reviewed by at least two reviewers, the composition of which includes PhDs, are well known in their circles. Author's part of the magazine includes both young scientists, graduate students and talented students, who publish their works, and famous giants of world science.

Subject areas:

  • Mathematics
    • Modeling and Simulation
    • Mathematical Physics
  • Computer Science
    • Computer Science (miscellaneous)

 

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Current Issue

Vol 30, No 2 (2022)

Articles

Numerical solution of Cauchy problems with multiple poles of integer order
Belov A.A., Kalitkin N.N.
Abstract

We consider Cauchy problem for ordinary differential equation with solution possessing a sequence of multiple poles. We propose the generalized reciprocal function method. It reduces calculation of a multiple pole to retrieval of a simple zero of accordingly chosen function. Advantages of this approach are illustrated by numerical examples. We propose two representative test problems which constitute interest for verification of other numerical methods for problems with poles.

Discrete and Continuous Models and Applied Computational Science. 2022;30(2):105-114
pages 105-114 views
Optimization of an isotropic metasurface on a substrate
Dombrovskaya Z.O.
Abstract

Mathematical statement of one-wavelength antireflective coating based on two-dimensional metamaterial is formulated for the first time. The constraints on geometric parameters of the structure are found. We propose a penalty function, which ensures the applicability of physical model and provides the uniqueness of the desired minimum. As an example, we consider the optimization of metasurface composed of PbTe spheres located on germanium substrate. It is shown that the accuracy of the minimization with properly chosen penalty term is the same as for the objective function without it.

Discrete and Continuous Models and Applied Computational Science. 2022;30(2):115-126
pages 115-126 views
Multistage pseudo-spectral method (method of collocations) for the approximate solution of an ordinary differential equation of the first order
Lovetskiy K.P., Kulyabov D.S., Hissein A.W.
Abstract

The classical pseudospectral collocation method based on the expansion of the solution in a basis of Chebyshev polynomials is considered. A new approach to constructing systems of linear algebraic equations for solving ordinary differential equations with variable coefficients and with initial (and/or boundary) conditions makes possible a significant simplification of the structure of matrices, reducing it to a diagonal form. The solution of the system is reduced to multiplying the matrix of values of the Chebyshev polynomials on the selected collocation grid by the vector of values of the function describing the given derivative at the collocation points. The subsequent multiplication of the obtained vector by the two-diagonal spectral matrix, ‘inverse’ with respect to the Chebyshev differentiation matrix, yields all the expansion coefficients of the sought solution except for the first one. This first coefficient is determined at the second stage based on a given initial (and/or boundary) condition. The novelty of the approach is to first select a class (set) of functions that satisfy the differential equation, using a stable and computationally simple method of interpolation (collocation) of the derivative of the future solution. Then the coefficients (except for the first one) of the expansion of the future solution are determined in terms of the calculated expansion coefficients of the derivative using the integration matrix. Finally, from this set of solutions only those that correspond to the given initial conditions are selected.

Discrete and Continuous Models and Applied Computational Science. 2022;30(2):127-138
pages 127-138 views
Complex eigenvalues in Kuryshkin-Wodkiewicz quantum mechanics
Zorin A.V., Malykh M.D., Sevastianov L.A.
Abstract

One of the possible versions of quantum mechanics, known as Kuryshkin-Wodkiewicz quantum mechanics, is considered. In this version, the quantum distribution function is positive, but, as a retribution for this, the von Neumann quantization rule is replaced by a more complicated rule, in which an observed value AA is associated with a pseudodifferential operator O^(A){\hat{O}(A)}. This version is an example of a dissipative quantum system and, therefore, it was expected that the eigenvalues of the Hamiltonian should have imaginary parts. However, the discrete spectrum of the Hamiltonian of a hydrogen-like atom in this theory turned out to be real-valued. In this paper, we propose the following explanation for this paradox. It is traditionally assumed that in some state ψ{\psi} the quantity AA is equal to λ{\lambda} if ψ{\psi} is an eigenfunction of the operator O^(A){\hat{O}(A)}. In this case, the variance O^((A-λ)2)ψ{\hat{O}((A-\lambda)2)\psi} is zero in the standard version of quantum mechanics, but nonzero in Kuryshkin’s mechanics. Therefore, it is possible to consider such a range of values and states corresponding to them for which the variance O^((A-λ)2){\hat{O}((A-\lambda)2)} is zero. The spectrum of the quadratic pencil O^(A2)-2O^(A)λ+λ2E^{\hat{O}(A2)-2\hat{O}(A)\lambda + \lambda 2 \hat{E}} is studied by the methods of perturbation theory under the assumption of small variance D^(A)=O^(A2)-O^(A)2{\hat{D}(A) = \hat{O}(A2) - \hat{O}(A) 2} of the observable AA. It is shown that in the neighborhood of the real eigenvalue λ{\lambda} of the operator  O^(A){\hat{O}(A)}, there are two eigenvalues of the operator pencil, which differ in the first order of perturbation theory by  ±iD^{\pm i \sqrt{\langle \hat{D} \rangle}}.

Discrete and Continuous Models and Applied Computational Science. 2022;30(2):139-148
pages 139-148 views
Investigation of adiabatic waveguide modes model for smoothly irregular integrated optical waveguides
Sevastyanov A.L.
Abstract

The model of adiabatic waveguide modes (AWMs) in a smoothly irregular integrated optical waveguide is studied. The model explicitly takes into account the dependence on the rapidly varying transverse coordinate and on the slowly varying horizontal coordinates. Equations are formulated for the strengths of the AWM fields in the approximations of zero and first order of smallness. The contributions of the first order of smallness introduce depolarization and complex values characteristic of leaky modes into the expressions of the AWM electromagnetic fields. A stable method is proposed for calculating the vertical distribution of the electromagnetic field of guided modes in regular multilayer waveguides, including those with a variable number of layers. A stable method for solving a nonlinear equation in partial derivatives of the first order (dispersion equation) for the thickness profile of a smoothly irregular integrated optical waveguide in models of adiabatic waveguide modes of zero and first orders of smallness is described. Stable regularized methods for calculating the AWM field strengths depending on vertical and horizontal coordinates are described. Within the framework of the listed matrix models, the same methods and algorithms for the approximate solution of problems arising in these models are used. Verification of approximate solutions of models of adiabatic waveguide modes of the first and zero orders is proposed; we compare them with the results obtained by other authors in the study of more crude models.

Discrete and Continuous Models and Applied Computational Science. 2022;30(2):149-159
pages 149-159 views
Analysis of queuing systems with threshold renovation mechanism and inverse service discipline
Zaryadov I.S., Viana H.C., Milovanova T.A.
Abstract

The paper presents a study of three queuing systems with a threshold renovation mechanism and an inverse service discipline. In the model of the first type, the threshold value is only responsible for activating the renovation mechanism (the mechanism for probabilistic reset of claims). In the second model, the threshold value not only turns on the renovation mechanism, but also determines the boundaries of the area in the queue from which claims that have entered the system cannot be dropped. In the model of the third type (generalizing the previous two models), two threshold values are used: one to activate the mechanism for dropping requests, the second - to set a safe zone in the queue. Based on the results obtained earlier, the main time-probabilistic characteristics of these models are presented. With the help of simulation modeling, the analysis and comparison of the behavior of the considered models were carried out.

Discrete and Continuous Models and Applied Computational Science. 2022;30(2):160-182
pages 160-182 views

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