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Exact Formula for Solving a Degenerate System of Quadratic Equations Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-04-22 Yu. G. Evtushenko, A. A. Tret’yakov
Abstract The paper is devoted to the solution of a nonlinear system of equations \(F(x{{) = 0}_{n}}\), where \(F\) is a quadratic mapping acting from \({{\mathbb{R}}^{n}}\) to \({{\mathbb{R}}^{n}}\). The derivative \(F{\kern 1pt} '\) is assumed to be degenerate at the solution point, which is a major characteristic property of nonlinearity of the mapping. Based on constructions of the p-regularity
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On the Construction of an Optimal Network of Observation Points when Solving Inverse Linear Problems of Gravimetry and Magnetometry Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-04-22 I. E. Stepanova, D. V. Lukyanenko, I. I. Kolotov, A. V. Shchepetilov, A. G. Yagola, A. N. Levashov
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On Asymptotics of the Solution to the Cauchy Problem for a Singularly Perturbed Operator-Differential Transport Equation with Weak Diffusion in the Case of Several Space Variables Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-04-22 A. V. Nesterov
Abstract A formal asymptotic expansion is constructed for the solution of the Cauchy problem for a singularly perturbed operator differential transport equation with small nonlinearities and weak diffusion in the case of several space variables. Under the conditions imposed on the data of the problem, the leading asymptotic term is described by the multidimensional generalized Burgers–Korteweg–de Vries
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Uniqueness of a Solution to the Lavrent’ev Integral Equation in n-Dimensional Space Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-04-22 M. M. Kokurin, V. V. Klyuchev, A. V. Gavrilova
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On the Probabilistic-Statistical Approach to the Analysis of Nonlocality Parameters of Plasma Density Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-04-22 N. S. Arkashov, V. A. Seleznev
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Algorithms for Optimizing Systems with Multiple Extremum Functionals Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-04-22 V. K. Tolstykh
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Boundary Value Problem of Calculating Ray Characteristics of Ocean Waves Reflected from Coastline Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-04-22 I. A. Nosikov, A. A. Tolchennikov, M. V. Klimenko
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Numerical Analysis for a Singularly Perturbed Parabolic Differential Equation with a Time Delay Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-04-22 Sisay Ketema Tesfaye, Tekle Gemechu Dinka, Mesfin Mekuria Woldaregay, Gemechis File Duressa
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Localizing the Initial Condition for Solutions of the Cauchy Problem for the Heat Equation Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-04-22 A. N. Konenkov
Abstract The Cauchy problem for the heat equation with zero right-hand side is considered. The initial function is assumed to belong to the space of tempered distributions. The problem of determining the support of the initial function from solution values at some fixed time \(T > 0\) is studied. Necessary and sufficient conditions for the support to lie in a given convex compact set are obtained.
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Algorithms for Solving the Inverse Scattering Problem for the Manakov Model Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-04-22 O. V. Belai, L. L. Frumin, A. E. Chernyavsky
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Sturm–Liouville Problem for a One-Dimensional Thermoelastic Operator in Cartesian, Cylindrical, and Spherical Coordinate Systems Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-04-22 A. V. Zemskov, D. V. Tarlakovskii
Abstract The problem of constructing eigenfunctions of a one-dimensional thermoelastic operator in Cartesian, cylindrical, and spherical coordinate systems is considered. The corresponding Sturm–Liouville problem is formulated using Fourier’s separation of variables applied to a coupled system of thermoelasticity equations, assuming that the heat transfer rate is finite. It is shown that the eigenfunctions
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Exponentially Convergent Numerical Scheme for the Stream Function of Potential Flow over Axisymmetric Bodies Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-04-22 A. G. Petrov
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Calculating a Perturbation of a Plasma Layer by an Electric Field Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-04-22 N. M. Gordeeva
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State Space Approach to Characterize Rayleigh Waves in Nonlocal Thermoelastic Medium with Double Porosity under Three-Phase-Lag Model Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-04-22 Chandra Sekhar Mahato, Siddhartha Biswas
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Kinetic Model of a Three-Component Plasma Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-04-22 M. V. Abgaryan, A. M. Bishaev
Abstract In this work, a system of kinetic equations is constructed to study the processes in a three-component plasma. It is an analogue of the Krook model, which is widely used in the dynamics of rarefied gases. The model is supposed to be used to study the processes in the channels of rocket electric thrusters.
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Stability and Error Analysis of an Efficient Numerical Method for Convection Dominated Parabolic PDEs with Jump Discontinuity in Source Function on Modified Layer-Adapted Mesh Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-04-22 Narendra Singh Yadav, Kaushik Mukherjee
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Target-Point Interpolation of a Program Control in the Approach Problem Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-04-22 A. V. Alekseev, A. A. Ershov
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Application of the Explicitly Iterative Scheme to Simulating Subsonic Reacting Gas Flows Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-04-01 E. E. Peskova, O. S. Yazovtseva
Abstract This paper is devoted to the study of the possibility of applying an explicitly iterative (local iterative modified—LI-M) scheme for calculating dissipative terms in the solution of problems of subsonic reacting flows with radical chain reactions, active diffusion processes, significant heat transfer, and energy absorption. Simulation of such flows is characterized by a restriction on the
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On the Solvability of an Essentially Nonlinear Elliptic Differential Equation with Nonlocal Boundary Conditions Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-04-01 O. V. Solonukha
Abstract Sufficient conditions for the existence of a generalized solution to a nonlinear elliptic differential equation with nonlocal boundary conditions of Bitsadze–Samarskii type are proved. The strong ellipticity condition is used for an auxiliary differential-difference operator. Under the formulated conditions, the differential-difference operator is demicontinuous, coercive, and has a semibounded
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Synthesis of an Optimal Stable Affine System Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-04-01 L. T. Ashchepkov
Abstract A method for constructing a feedback that ensures the attraction of trajectories of an affine system to an equilibrium state and to a given manifold is proposed. The feedback is found in an analytical form as a solution to an auxiliary optimal control problem. Sufficient conditions for the existence of the optimal control are given. Application of the proposed method to some classes of linear
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Explicit Numerically Implementable Formulas for Poincaré–Steklov Operators Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-04-01 A. S. Demidov, A. S. Samokhin
Abstract The paper presents explicit numerically implementable formulas for the Poincaré–Steklov operators, such as the Dirichlet–Neumann, Dirichlet–Robin, Robin1–Robin2, and Grinberg–Mayergoiz operators, related to the two-dimensional Laplace equation. These formulas are based on the lemma about a univalent isometric mapping of a closed analytic curve onto a circle. Numerical results for domains with
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Solution to a Two-Dimensional Nonlinear Parabolic Heat Equation Subject to a Boundary Condition Specified on a Moving Manifold Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-04-01 A. L. Kazakov, O. A. Nefedova, L. F. Spevak
Abstract This paper is devoted to the study of a degenerating parabolic heat equation with nonlinearities of a general type in the presence of a source (sink) in the case of two spatial variables. The problem of initiating a heat wave propagating over a cold (zero) background with a finite velocity and a boundary condition specified on a moving manifold—a closed line—is considered. For this problem
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Smooth Lyapunov Manifolds for Autonomous Systems of Nonlinear Ordinary Differential Equations and Their Application to Solving Singular Boundary Value Problems Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-04-01 N. B. Konyukhova
Abstract For an autonomous system of \(N\) nonlinear ordinary differential equations considered on a semi-infinite interval \({{T}_{0}} \leqslant t < \infty \) and having a (pseudo)hyperbolic equilibrium point, the paper considers an \(n\)-dimensional \((0 < n < N)\) stable solution manifold, or a manifold of conditional Lyapunov stability, which, for each sufficiently large \(t\), exists in the phase
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Estimation of QTT Ranks of Regular Functions on a Uniform Square Grid Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-04-01 A. Zyl’, N. Zamarashkin
Abstract The paper proves estimates of \(\varepsilon \)-ranks for TT decompositions of tensors obtained by tensorizing the values of a regular function of one complex variable on a uniform square grid in the complex plane. A relation between the approximation accuracy and the geometry of the domain of regularity of the function is established.
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Numerical Analysis of the Blow-Up of One-Dimensional Polymer Fluid Flow with a Front Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-03-21 L. S. Bryndin, B. V. Semisalov, V. A. Beliaev, V. P. Shapeev
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Integral Representations for Second-Order Elliptic Systems in the Plane Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-03-21 A. P. Soldatov
Abstract A fundamental solution matrix for elliptic systems of the second order with constant leading coefficients is constructed. It is used to obtain an integral representation of functions belonging to the Hölder class in a closed domain with a Lyapunov boundary. In the case of an infinite domain, these functions have power-law asymptotics at infinity. The representation is used to study a mixed-contact
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Improving the Accuracy of Exponentially Converging Quadratures Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-03-21 A. A. Belov, V. S. Khokhlachev
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Gaps in the Spectrum of Thin Waveguides with Periodically Locally Deformed Walls Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-03-21 S. A. Nazarov
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Order-Optimal Spline Methods for Solving Singular Integro-Differential Equations Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-03-21 N. S. Gabbasov
Abstract A linear integro-differential equation with a singular differential operator in the principal part is studied. For its approximate solution in the space of generalized functions, special generalized versions of spline methods are proposed and justified. The optimality in the order of accuracy of the methods constructed is established.
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Actual Accuracy of Linear Schemes of High-Order Approximation in Gasdynamic Simulations Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-03-21 M. D. Bragin
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Convergence of Some Difference Schemes of the Support Operator Method for Repeated Rotational Operations Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-03-21 Yu. A. Poveshchenko, A. Yu. Krukovskii, V. O. Podryga, P. I. Rahimly
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Simulation of Domain Walls: Simple Waves in the Magnetodynamics Equation Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-03-21 L. A. Kalyakin, E. G. Ekomasov
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Multiplicative Control Problem for a Nonlinear Reaction–Diffusion Model Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-03-21 R. V. Brizitskii, A. A. Donchak
Abstract The paper studies a multiplicative control problem for the reaction–diffusion equation in which the reaction coefficient nonlinearly depends on the substance concentration, as well as on spatial variables. The role of multiplicative controls is played by the coefficients of diffusion and mass transfer. The solvability of the extremum problem is proved, and optimality systems are derived for
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Deriving Known Particular Solutions of the σ-Commutation Problem (σ ≠ 0, ±1) for a Toeplitz and a Hankel Matrix within a Unified Approach Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-03-21 V. N. Chugunov, Kh. D. Ikramov
In their preceding publication, the authors proposed a unified approach to the construction of matrix pairs \((T,H)\) that solve the \(\sigma \)-commutation problem for Toeplitz and Hankel matrices. Here, this approach is applied to the derivation of two classes of solutions that were earlier found by V.N. Chugunov from entirely different considerations.
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Approximation of Continuous Functions by Classical Sincs and Values of Operators Cλ Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-02-01
Abstract The properties of sinc approximations are considered. Previously used classical sinc-approximations provide poor approximation quality, while a new operator generalizing sinc approximations yields better results. The numerical implementation of an experiment is presented in plots.
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Erratum to: Triple Series Evaluated in π and $$\ln 2$$ as well as Catalan’s Constant G Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-02-01
An Erratum to this paper has been published: https://doi.org/10.1134/S0965542524020155
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Improved Quadrature Formulas for the Direct Value of the Normal Derivative of a Single-Layer Potential Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-02-01
Abstract A single-layer potential for the Helmholtz equation in the three-dimensional case and a single-layer potential for the Laplace equation are considered. A quadrature rule is derived for the direct value of the normal derivative of the single-layer potential with a continuous density given on a closed or open surface. The quadrature rule provides a much higher accuracy than previously available
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Algorithm for Solving the Four-Wave Kinetic Equation in Problems of Wave Turbulence Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-02-01
Abstract We propose the method for numerical solution of four-wave kinetic equations that arise in the wave turbulence (weak turbulence) theory when describing a homogeneous isotropic interaction of waves. To calculate the collision integral in the right-hand side of equation, the cubature formulas of high rate of convergence are developed, which allow for adaptation of the algorithm to the singularities
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New Computer Efficient Approximations of Random Functions for Solving Stochastic Transport Problems Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-02-01
Abstract A new grid approximation of a homogeneous isotropic random field with a given average correlation length is developed. The approximation is constructed by partitioning the coordinate space into an ensemble of cubes whose size reproduces the average correlation length in the case of a field value chosen independently from a given one-dimensional distribution in each partition element. The correlative
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Tenth-Order Accurate Numerical Method for Solving the Time-Dependent Schrödinger Equation Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-02-01
Abstract A tenth-order accurate method for the numerical solution of the time-dependent Schrödinger equation is presented. The method is based on the approximation of the evolution operator by a product formula. A decrease in the number of operator exponentials in the resulting formula due to the optimization of their sequence is discussed. Based on the idea proposed by Yoshida, two tenth-order accurate
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Local Wavelet Adaptation of Cartesian Grids in Computational Fluid Dynamics Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-02-01
Abstract A method for dynamic local adaptation of graded Cartesian trees for the numerical solution of fluid dynamics problems is presented. Local wavelet analysis of a gas-dynamic field based on nonuniform B-splines is applied independently to each cell of the computational grid and makes it possible to identify nonsmooth or significantly nonlinear sections of the solution (or, vice versa, sufficiently
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Stability and Error Estimates of High Order BDF-LDG Discretizations for the Allen–Cahn Equation Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-01-29 Fengna Yan, Ziqiang Cheng
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Singularity Formation in an Incompressible Boundary Layer on an Upstream Moving Wall under Given External Pressure Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-01-29 S. I. Bezrodnykh, V. B. Zametaev, Te Ha Chzhun
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Generalization of the Penalized Wall Function Method for Modeling of Turbulent Flows with Adverse Pressure Gradient Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-01-29 O. V. Vasilyev, N. S. Zhdanova
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On the Simulation of a Rarefied Plasma Jet on the Basis of Kinetic Equations Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-01-29 M. V. Abgaryan, A. M. Bishaev, V. A. Rykov
Abstract The problem of a rarefied plasma jet emerging from a stationary plasma engine is considered. The consideration is carried out entirely at the kinetic level; namely, the motion of all plasma components is described in terms of distribution functions. The system of kinetic equations should be solved together with Maxwell’s equations. Methods for solving the resulting problem are discussed.
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Data Parallelization Algorithms for the Direct Simulation Monte Carlo Method for Rarefied Gas Flows on the Basis of OpenMP Technology Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-01-29 N. Yu. Bykov, S. A. Fyodorov
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A Novel Fitted Method for a Class of Singularly Perturbed Differential-Difference Equations with Small Delay Exhibiting Twin Layer or Oscillatory Behaviour Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-01-29 Mohammad Javed Alam, Hari Shankar Prasad, Rakesh Ranjan
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Accelerating the Solution of the Boltzmann Equation by Controlling Contributions to the Collision Integral Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-01-29 F. G. Tcheremissine
Abstract A method of reducing the number of arithmetic operations needed to evaluate the Boltzmann collision integral by the conservative projection method is proposed. This is achieved by eliminating the contributions that are less than a certain threshold. An estimate of the maximum magnitude of this threshold is given. For four such thresholds that differ by an order of magnitude from each other
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Study of Nonclassical Transport by Applying Numerical Methods for Solving the Boltzmann Equation Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-01-29 V. V. Aristov, I. V. Voronich, S. A. Zabelok
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Multipole Representation of the Gravitational Field of the Asteroid (16) Psyche Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-01-29 V. I. Nikonov
Abstract An approach to calculating multipole approximations of the gravitational potential of small celestial bodies with an irregular mass distribution is demonstrated for the asteroid (16) Psyche as an example.
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Nonclassical Heat Transfer in a Microchannel and a Problem for Lattice Boltzmann Equations Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-01-29 O. V. Ilyin
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Study of the Gardner Equation with Homogeneous Boundary Conditions via Fourth Order Modified Cubic B-Spline Collocation Method Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-01-29 S. Dahiya, A. Singh, S. P. Singh
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Numerical Analysis of Rarefied Gas Flow through a System of Short Channels Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-01-29 I. V. Voronich, V. A. Titarev
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Projection-Grid Schemes on Irregular Grids for a Parabolic Equation Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-01-29 O. G. Olkhovskaya
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Stability Analysis of Polymerization Fronts Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-01-29 Y. Joundy, H. Rouah, A. Taik
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Convergence of a Numerical Method for Solving the Optimal Control Problem of Panel Forming under Creep Conditions Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-01-01
Abstract A dynamic programming method is used for the numerical solution of optimal control problems for forming structural elements under creep conditions. The method is implemented in a finite-element software package. The stability of the method is analyzed.
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Projector Approach to the Butuzov–Nefedov Algorithm for Finding Asymptotic Solutions for a Class of Discrete Problems with a Small Step Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-01-01
Abstract V.F. Butuzov and N.N. Nefedov proposed an algorithm for constructing asymptotics with boundary functions of two types for solving a discrete initial value problem with a small step \({{\varepsilon }^{2}}\) and a nonlinear term of order \(\varepsilon \) in the critical case, i.e., when the degenerate equation with \(\varepsilon = 0\) is not solvable uniquely for the unknown variable. In this
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Sensitivity of the Functionals of the Variational Data Assimilation Problem when Reconstructing the Initial State and Heat Flux for a Model of Sea Thermodynamics Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2024-01-01
Abstract The paper considers the problem of variational assimilation of observational data in order to reconstruct the initial state and heat fluxes for the mathematical model of sea thermodynamics developed at the Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences. The sensitivity of the functionals of the solution to the input data on the heat flux on the sea surface in the considered
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Formulas for Computing Euler-Type Integrals and Their Application to the Problem of Constructing a Conformal Mapping of Polygons Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2023-12-25 S. I. Bezrodnykh
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Solving Nonlinear Volterra Integral Equations of the First Kind with Discontinuous Kernels by Using the Operational Matrix Method Comput. Math. Math. Phys. (IF 0.7) Pub Date : 2023-12-25 Simin Aghaei Amirkhizi, Yaghoub Mahmoudi, Ali Salimi Shamloo