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Excitation of Seismoacoustic Waves from a Singular Source Acting on the Boundary of a Liquid Layer and a Poroelastic Half-Space Numer. Analys. Appl. Pub Date : 2024-03-13 Kh. Kh. Imomnazarov, A. A. Mikhailov, K. S. Goziev, A. T. Omonov
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A New A Posteriori Error Estimates for Optimal Control Problems Governed by Parabolic Integro-Differential Equations Numer. Analys. Appl. Pub Date : 2024-03-13 H. Chen, T. Hou
Abstract In this paper, we provide a new a posteriori error analysis for linear finite element approximation of a parabolic integro-differential optimal control problem. The state and co-state are approximated by piecewise linear functions, while the control variable is discretized by variational discretization method. We first define the elliptic reconstructions of numerical solutions and then discuss
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On the Fourth Order Accurate Interpolation Operator for the Difference Solution of the 3-Dimensional Laplace Equation Numer. Analys. Appl. Pub Date : 2024-03-13 A. A. Dosiyev, E. Celiker
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Sensitivity of Functionals to Input Data in a Variational Assimilation Problem for a Sea Thermodynamics Model Numer. Analys. Appl. Pub Date : 2024-03-13 V. P. Shutyaev, E. I. Parmuzin
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An Inverse Problem for an Age-Structured Population Dynamics Model with Migration Flows Numer. Analys. Appl. Pub Date : 2024-03-13 A. Yu. Shcheglov, S. V. Netessov
Abstract An inverse problem of reconstructing a coefficient in the differential equation of a model of development for a homogeneous biological population of organisms structured by age is considered. The model takes into account the impact of migration flows on population size changes. Conditions are established to ensure the uniqueness of the solution of the inverse problem. A brief overview of algorithms
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Estimates of CPU Load Unbalancing in Parallelizing Solutions of $$3D$$ Boundary Value Problems on Quasi-Structured Grids Numer. Analys. Appl. Pub Date : 2024-03-13 Il. A. Klimonov, V. D. Korneev, V. M. Sveshnikov
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Numerical and Mathematical Modeling of a Gene Network with Nonlinear Degradation of the Components Numer. Analys. Appl. Pub Date : 2024-03-13 V. P. Golubyatnikov, N. E. Kirillova, L. S. Minushkina
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Analyzing the Semilocal Convergence of a Fourth-Order Newton-Type Scheme with Novel Majorant and Average Lipschitz Conditions Numer. Analys. Appl. Pub Date : 2024-03-13 J. P. Jaiswal
Abstract The main focus of this paper is the analysis of the semilocal convergence (S.C.) of a three-step Newton-type scheme (TSNTS) used for finding the solution of nonlinear operators in Banach spaces (B.S.). A novel S.C. analysis of the TSNTS is introduced, which is based on the assumption that a generalized Lipschitz condition (G.L.C.) is satisfied by the first derivative of the operator. The findings
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Investigation of Overexponential Growth of Mean Particle Flux with Multiplication in Random Medium Numer. Analys. Appl. Pub Date : 2023-12-07 G. Z. Lotova, G. A. Mikhailov
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Involutions and Coninvolutions Numer. Analys. Appl. Pub Date : 2023-12-07 Kh. D. Ikramov
Abstract A review of the relatively little-known matrix class, called coninvolutions, is given. The properties of these matrices are compared with those of the well studied involutory matrices or, briefly, involutions.
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Stochastic Simulation Algorithms for Iterative Solution of the Lamé Equation Numer. Analys. Appl. Pub Date : 2023-12-07 I. A. Aksyuk, A. E. Kireeva, K. K. Sabelfeld, D. D. Smirnov
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An Approximate Iterative Algorithm for Modeling of Non-Gaussian Vectors with Given Marginal Distributions and Covariance Matrix Numer. Analys. Appl. Pub Date : 2023-12-07 M. S. Akenteva, N. A. Kargapolova, V. A. Ogorodnikov
Abstract A new iterative method for modeling of non-Gaussian random vectors with given marginal distributions and a covariance matrix is proposed in this paper. The algorithm is compared with another iterative algorithm for modeling of non-Gaussian vectors, based on reordering of a sample of independent random variables with given marginal distributions. Our numerical studies show that both algorithms
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Search for the Best Cubature Formulas on the Sphere Invariant under the Icosahedral Rotation Group Numer. Analys. Appl. Pub Date : 2023-12-07 A. S. Popov
Abstract A process of searching on the sphere for the best (in a sense) cubature formulas that are invariant under the transformations of the icosahedral rotation group is described. The parameters of the best cubature formulas of this symmetry type up to the 30th order of accuracy are given to 16 significant digits. A table which contains the main characteristics of all the best to date cubature formulas
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Calculation of Flows of Gas-Liquid Mixtures by a Modified Nodal Method of Characteristics Numer. Analys. Appl. Pub Date : 2023-12-07 V. S. Surov
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On the Properties of Difference Schemes for Solving Nonlinear Dispersive Equations of Increased Accuracy. I. The Case of One Spatial Variable Numer. Analys. Appl. Pub Date : 2023-12-07 Z. I. Fedotova, G. S. Khakimzyanov
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Using a Low Dissipation Lax–Friedrichs Scheme for Numerical Modeling of Relativistic Flows Numer. Analys. Appl. Pub Date : 2023-12-07 I. M. Kulikov, D. A. Karavaev
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Estimation of the Phase Probability Density Function by Solving the Inverse Problem Numer. Analys. Appl. Pub Date : 2023-09-20 M. L. Maslakov, V. V. Egorov
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Study of Superexponential Growth of the Mean Particle Flux by Monte Carlo Method Numer. Analys. Appl. Pub Date : 2023-09-20 G. Z. Lotova, G. A. Mikhailov
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A Trigonometric Quintic B-Spline Basis Collocation Method for the KdV–Kawahara Equation Numer. Analys. Appl. Pub Date : 2023-09-20 B. Karaagac, A. Esen, K. M. Owolabi, E. Pindza
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Monte Carlo Simulation of Laser Navigation System Signals Numer. Analys. Appl. Pub Date : 2023-09-20 E. G. Kablukova, V. G. Oshlakov, S. M. Prigarin
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LBM without Interpolation on Non-Uniform Grids Numer. Analys. Appl. Pub Date : 2023-09-20 A. V. Berezin, A. V. Ivanov, A. Yu. Perepelkina
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A Refinement Sum-Technique in an Iterative Scheme Adapted for a Linear System of Integral Equations to Approach a Fredholm Integral Equation’s Solution Numer. Analys. Appl. Pub Date : 2023-09-20 M. G. Mahcene, A. Khellaf, S. Lemita, M. Z. Aissaoui
Abstract Based on the use of the Geometric Series Theorem, we transform a linear Fredholm integral equation of the second kind defined on a large interval into an equivalent linear system of Fredholm integral equations of the second kind; then, we inflict a refinement in the way the investigated generalized iterative scheme approximates the sought-after solution. By avoiding to inverse a bounded linear
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A Priori Error Bounds for Parabolic Interface Problems with Measure Data Numer. Analys. Appl. Pub Date : 2023-09-20 J. Sen Gupta
Abstract This article studies a priori error analysis for linear parabolic interface problems with measure data in time in a bounded convex polygonal domain in \(\mathbb{R}^2\). Both the spatially discrete and the fully discrete approximations are analyzed. We have used the standard continuous fitted finite element discretization for the space while, the backward Euler approximation is used for the
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A Dual Method for Solving an Equilibrium Problem of a Body Containing a Thin Defect Numer. Analys. Appl. Pub Date : 2023-07-11 A. V. Zhiltsov, N. N. Maksimova
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Error Estimators and Their Analysis for CG, Bi-CG, and GMRES Numer. Analys. Appl. Pub Date : 2023-07-11 P. Jain, K. Manglani, M. Venkatapathi
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Convergence Analysis of Multi-Step Collocation Methods to Solve Generalized Auto-Convolution Volterra Integral Equations Numer. Analys. Appl. Pub Date : 2023-07-11 P. Darania, S. Pishbin, A. Ebadi
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Linear Quasi-Monotone and Hybrid Grid-Characteristic Schemes for the Numerical Solution of Linear Acoustic Problems1 Numer. Analys. Appl. Pub Date : 2023-07-11 E. K. Guseva, V. I. Golubev, I. B. Petrov
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An Implicit Iteration Method for Solving Linear Ill-Posed Operator Equations Numer. Analys. Appl. Pub Date : 2023-07-11 T. Bechouat
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Pseudo-Commutation Classes of Complex Matrices and Their Decomplexification Numer. Analys. Appl. Pub Date : 2023-07-11 Kh. D. Ikramov
Abstract The relation between complex matrices \(H\) and \(A\) given by the equality \(HA = \overline {A} H\) is called the pseudo-commutation. The set \(S_H\) of all \(A\) that pseudo-commute with a nonsingular \(n\times n\) matrix \(H\) is called the pseudo-commutation class defined by \(H\). Every class \(S_H\) is a subspace of the space \(M_n({\bf C})\) interpreted as a real vector space of dimension
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Exact Calculation of the Approximation Error of Multiple Itô Stochastic Integrals1 Numer. Analys. Appl. Pub Date : 2023-07-11 K. A. Rybakov
Abstract In the article, formulas for exact calculation of the approximation error of multiple Itô stochastic integrals based on an orthogonal expansion are obtained. As an example, Itô stochastic integrals of multiplicity 2–4 used in numerical methods for solving stochastic differential equations with strong convergence of order 1–2 are considered.
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Non-Traditional Intervals and Their Use. Which Ones Really Make Sense? Numer. Analys. Appl. Pub Date : 2023-07-11 S. P. Shary
Abstract The paper discusses the question of why intervals, which are the main object of Interval Analysis, have exactly the form that we know well and habitually use, and not some other. In particular, we investigate why traditional intervals are closed, i.e., contain their endpoints, and also what is wrong with an empty interval. A second question considered in the work is how expedient it is to
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A Local Ensemble Data Assimilation Algorithm for Nonlinear Geophysical Models Numer. Analys. Appl. Pub Date : 2023-03-21 E. G. Klimova
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A Piecewise-Parabolic Reconstruction of the Physical Variables in a Low-Dissipation HLL Method for the Numerical Solution of the Equations of Special Relativistic Hydrodynamics Numer. Analys. Appl. Pub Date : 2023-03-21 I. M. Kulikov, D. A. Karavaev
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A Posteriori Error Majorants for FEM Solutions of Plate Bending Problem upon Winkler Subgrade1 Numer. Analys. Appl. Pub Date : 2023-03-21 V. G. Korneev
Abstract The paper is devoted to the mixed finite element method for the equation \(\Delta\Delta u+ \kappa^2 u=f\), \(x \in\Omega\), with boundary conditions \(u= \partial u/ \partial {\boldsymbol\nu }= 0\) on \(\partial \Omega\), where \({\boldsymbol\nu }\) is the normal to the boundary and \(\kappa \ge 0\) is an arbitrary constant on each finite element. At \(\kappa\equiv 0\) residual type a posteriori
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Formulas for Numerical Differentiation of Functions with Large Gradients1 Numer. Analys. Appl. Pub Date : 2023-03-21 A. I. Zadorin
Abstract Numerical differentiation of functions with large gradients is investigated. It is assumed that such a function contains a component known up to a factor and responsible for the large gradients of the function. Application of classical formulas for calculating derivatives to such functions may lead to significant errors. For the numerical differentiation on a uniform grid, special-purpose
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Stability Domains of an Implicit Method for the Numerical Solution of Abel Type Integral Algebraic Equations Numer. Analys. Appl. Pub Date : 2023-03-21 O. S. Budnikova, M. N. Botoroeva, G. K. Sokolova
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Unsteady Concentration Field of a Reacting Gas in the Vicinity of a Burning Coal Particle Numer. Analys. Appl. Pub Date : 2023-03-21 S. V. Cherdantsev, P. A. Shlapakov, S. I. Goloskokov, K. S. Lebedev, A. Yu. Erastov
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A Source Configuration Leading to Accumulation of Tsunami Wave Energy Near a Round Island Numer. Analys. Appl. Pub Date : 2023-03-21 An. G. Marchuk, E. D. Moskalensky
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On the Sensitivity of the Canonical Angles of a Unitoid Matrix Numer. Analys. Appl. Pub Date : 2022-12-08 Kh. D. Ikramov, A. M. Nazari
Abstract A unitoid matrix is a square complex matrix that can be brought to diagonal form by a Hermitian congruence transformation. The canonical angles of a nonsingular unitoid matrix \(A\) are (up to the factor 1/2) the arguments of the eigenvalues of the cosquare of \(A\), which is the matrix \(A^{-*}A\). We derive an estimate for the derivative of an eigenvalue of the cosquare in the direction
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Solving the Pure Neumann Problem by a Mixed Finite Element Method Numer. Analys. Appl. Pub Date : 2022-12-08 M. I. Ivanov, I. A. Kremer, Yu. M. Laevsky
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On Discretization of the Evolution p-Bi-Laplace Equation Numer. Analys. Appl. Pub Date : 2022-12-08 M. Djaghout, A. Chaoui, K. Zennir
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On the Variance of Estimation of a Diffusion Process Functional in a Domain with a Reflecting Boundary Numer. Analys. Appl. Pub Date : 2022-12-08 S. A. Gusev
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Estimation of Pointwise Approximation Error Using a Set of Numerical Solutions Numer. Analys. Appl. Pub Date : 2022-12-08 A. K. Alekseev, A. E. Bondarev
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Erratum to: On a Numerical Model of a Circadian Oscillator Numer. Analys. Appl. Pub Date : 2022-12-08 A. A Akinshin, N. B Ayupova, V. P Golubyatnikov, N. E Kirillova, O. A Podkolodnaya, N. L Podkolodnyy
An Erratum to this paper has been published: https://doi.org/10.1134/S1995423922040103
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Erratum to: On a Method of Constructing Quadrature Formulas for Computing Hypersingular Integrals Numer. Analys. Appl. Pub Date : 2022-12-08 I. V Boikov, A. I Boikova
An Erratum to this paper has been published: https://doi.org/10.1134/S1995423922040115
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Erratum to: On the Advantages of Nonstandard Finite Difference Discretizations for Differential Problems Numer. Analys. Appl. Pub Date : 2022-12-08 D. Conte, N. Guarino, G. Pagano, B. Paternoster
An Erratum to this paper has been published: https://doi.org/10.1134/S1995423922040127
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New Convergence Mode For Generalized Spectrum Approximation Numer. Analys. Appl. Pub Date : 2022-12-08 S. Kamouche, H. Guebbai
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Stability Domains of Explicit Multistep Methods Numer. Analys. Appl. Pub Date : 2022-12-08 I. V. Kireev, A. E. Novikov, E. A. Novikov
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Experimental Study of Some Solvers of 3D Boundary Value Subproblems on Regular Subgrids of Quasi-Structured Parallelepipedal Grids Numer. Analys. Appl. Pub Date : 2022-12-08 I. A. Klimonov, V. M. Sveshnikov
Abstract An experimental study of the efficiency of 3D boundary value problem solvers on regular subgrids of quasi-structured parallelepipedal grids is carried out. Five solvers are considered. Three of them are iterative ones: successive over-relaxation, alternating direction implicit, and explicit incomplete factorization with acceleration by conjugate gradients, and two are direct ones: PARDISO
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Uniqueness Conditions and Numerical Approximation of the Solution to M. M. Lavrentiev’s Integral Equation Numer. Analys. Appl. Pub Date : 2022-12-08 M. Yu. Kokurin, V. V. Klyuchev
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On a Method of Constructing Quadrature Formulas for Computing Hypersingular Integrals Numer. Analys. Appl. Pub Date : 2022-08-26 I. V Boikov, A. I Boikova
Abstract This paper is devoted to constructing quadrature formulas for evaluating singular and hypersingular integrals. For evaluating integrals with weights \((1-t)^{\gamma_1}(1+t)^{\gamma_2}\), \(\gamma_1, \gamma_2>-1\) defined on \([-1,1]\) we have constructed quadrature formulas uniformly converging on [\(-1,1\)] to the original integral with weights \((1-t)^{\gamma_1} (1+t)^{\gamma_2}\), \(\gamma_1
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On a Numerical Model of a Circadian Oscillator Numer. Analys. Appl. Pub Date : 2022-08-26 A. A Akinshin, N. B Ayupova, V. P Golubyatnikov, N. E Kirillova, O. A Podkolodnaya, N. L Podkolodnyy
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Finite Difference Schemes of 4th Order Approximation for Maxwell’s Equations Numer. Analys. Appl. Pub Date : 2022-08-26 A. F Mastryukov
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An Implicit Multilayer Parallel Algorithm for a Multidimensional Wave Equation Numer. Analys. Appl. Pub Date : 2022-08-26 S. D. Algazin
Abstract A numerical algorithm without saturation for a wave equation is considered. It is assumed that the Laplace operator has a real discrete spectrum and the corresponding matrix of the discrete Laplace operator has a complete set of eigenvectors. The technique is explained by the example of a one-dimensional equation. However, it is shown that here the dimension is insignificant.
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Monte Carlo Simulation of Ring-Shaped Structures of Laser Pulse Radiation Scattered in Atmospheric Clouds and Water Media Numer. Analys. Appl. Pub Date : 2022-08-26 S. M Prigarin, D. E. Mironova
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Fitted Operator Method over Gaussian Quadrature Formula for Parabolic Singularly Perturbed Convection-Diffusion Problem Numer. Analys. Appl. Pub Date : 2022-08-26 D. M. Tefera, A. A. Tiruneh, G. A. Derese
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Generalization of the Gauss–Jordan Method for Solving Homogeneous Infinite Systems of Linear Algebraic Equations Numer. Analys. Appl. Pub Date : 2022-08-26 F. M Fedorov, N. N Pavlov, S. V Potapova, O. F Ivanova, V. Yu Shadrin
Abstract In this paper, first, using reduction in a narrow sense (the simple reduction method), we have generalized the classical Gauss–Jordan method for solving finite systems of linear algebraic equations to inhomogeneous infinite systems. The generalization is based on a new theory of solving inhomogeneous infinite systems proposed by us, which gives an exact analytical solution in the form of a
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On the Advantages of Nonstandard Finite Difference Discretizations for Differential Problems Numer. Analys. Appl. Pub Date : 2022-08-26 D. Conte, N. Guarino, G. Pagano, B. Paternoster