Subjects -> MATHEMATICS (Total: 1100 journals)
    - APPLIED MATHEMATICS (88 journals)
    - GEOMETRY AND TOPOLOGY (23 journals)
    - MATHEMATICS (812 journals)
    - MATHEMATICS (GENERAL) (43 journals)
    - NUMERICAL ANALYSIS (24 journals)

MATHEMATICS (812 journals)            First | 1 2 3 4 5     

Showing 401 - 538 of 538 Journals sorted alphabetically
Journal of Computational Physics     Hybrid Journal   (Followers: 70)
Journal of Computational Physics : X     Open Access   (Followers: 1)
Journal of Computer Engineering, System and Science (CESS)     Open Access  
Journal of Contemporary Mathematical Analysis     Hybrid Journal  
Journal of Cryptology     Hybrid Journal   (Followers: 3)
Journal of Difference Equations and Applications     Hybrid Journal  
Journal of Differential Equations     Full-text available via subscription   (Followers: 1)
Journal of Discrete Algorithms     Hybrid Journal   (Followers: 4)
Journal of Discrete Mathematics     Open Access   (Followers: 1)
Journal of Dynamics and Differential Equations     Hybrid Journal  
Journal of Engineering Mathematics     Hybrid Journal   (Followers: 2)
Journal of Evolution Equations     Hybrid Journal  
Journal of Experimental Algorithmics     Full-text available via subscription   (Followers: 1)
Journal of Flood Risk Management     Hybrid Journal   (Followers: 13)
Journal of Formalized Reasoning     Open Access   (Followers: 2)
Journal of Function Spaces     Open Access  
Journal of Functional Analysis     Full-text available via subscription   (Followers: 2)
Journal of Geochemical Exploration     Hybrid Journal   (Followers: 1)
Journal of Geological Research     Open Access   (Followers: 1)
Journal of Geovisualization and Spatial Analysis     Hybrid Journal  
Journal of Global Optimization     Hybrid Journal   (Followers: 6)
Journal of Global Research in Mathematical Archives     Open Access   (Followers: 1)
Journal of Group Theory     Hybrid Journal   (Followers: 2)
Journal of Homotopy and Related Structures     Hybrid Journal  
Journal of Honai Math     Open Access  
Journal of Humanistic Mathematics     Open Access   (Followers: 1)
Journal of Hyperbolic Differential Equations     Hybrid Journal  
Journal of Indian Council of Philosophical Research     Hybrid Journal  
Journal of Industrial Mathematics     Open Access   (Followers: 2)
Journal of Inequalities and Applications     Open Access  
Journal of Infrared, Millimeter and Terahertz Waves     Hybrid Journal   (Followers: 2)
Journal of Integrable Systems     Open Access   (Followers: 1)
Journal of K-Theory     Full-text available via subscription  
Journal of Knot Theory and Its Ramifications     Hybrid Journal   (Followers: 1)
Journal of Kufa for Mathematics and Computer     Open Access   (Followers: 1)
Journal of Liquid Chromatography & Related Technologies     Hybrid Journal   (Followers: 7)
Journal of Logical and Algebraic Methods in Programming     Hybrid Journal  
Journal of Manufacturing Systems     Full-text available via subscription   (Followers: 4)
Journal of Mathematical Analysis and Applications     Full-text available via subscription   (Followers: 4)
Journal of mathematical and computational science     Open Access   (Followers: 7)
Journal of Mathematical and Fundamental Sciences     Open Access  
Journal of Mathematical Behavior     Hybrid Journal   (Followers: 2)
Journal of Mathematical Chemistry     Hybrid Journal   (Followers: 3)
Journal of Mathematical Cryptology     Hybrid Journal   (Followers: 1)
Journal of Mathematical Extension     Open Access   (Followers: 3)
Journal of Mathematical Finance     Open Access   (Followers: 8)
Journal of Mathematical Imaging and Vision     Hybrid Journal   (Followers: 6)
Journal of Mathematical Logic     Hybrid Journal   (Followers: 2)
Journal of Mathematical Modelling and Algorithms     Hybrid Journal   (Followers: 1)
Journal of Mathematical Neuroscience     Open Access   (Followers: 10)
Journal of Mathematical Sciences     Hybrid Journal  
Journal of Mathematical Sciences and Applications     Open Access   (Followers: 2)
Journal of Mathematical Sociology     Hybrid Journal   (Followers: 3)
Journal of Mathematics     Open Access  
Journal of Mathematics and Statistics     Open Access   (Followers: 8)
Journal of Mathematics and the Arts     Hybrid Journal   (Followers: 2)
Journal of Mathematics Education at Teachers College     Open Access   (Followers: 2)
Journal of Mathematics in Industry     Open Access  
Journal of Mathematics Research     Open Access   (Followers: 6)
Journal of Metallurgy     Open Access   (Followers: 7)
Journal of Modern Mathematics Frontier     Open Access  
Journal of Multidisciplinary Modeling and Optimization     Open Access  
Journal of Multivariate Analysis     Hybrid Journal   (Followers: 13)
Journal of Natural Sciences and Mathematics Research     Open Access  
Journal of Nonlinear Analysis and Optimization : Theory & Applications     Open Access   (Followers: 4)
Journal of Nonlinear Mathematical Physics     Hybrid Journal   (Followers: 1)
Journal of Nonlinear Science     Hybrid Journal   (Followers: 1)
Journal of Numerical Cognition     Open Access  
Journal of Numerical Mathematics     Hybrid Journal   (Followers: 2)
Journal of Optimization     Open Access   (Followers: 4)
Journal of Peridynamics and Nonlocal Modeling     Hybrid Journal  
Journal of Problem Solving     Open Access   (Followers: 2)
Journal of Progressive Research in Mathematics     Open Access   (Followers: 1)
Journal of Pseudo-Differential Operators and Applications     Hybrid Journal  
Journal of Pure and Applied Algebra     Full-text available via subscription   (Followers: 4)
Journal of Quantitative Analysis in Sports     Hybrid Journal   (Followers: 8)
Journal of Quantitative Linguistics     Hybrid Journal   (Followers: 6)
Journal of Scientific Computing     Hybrid Journal   (Followers: 18)
Journal of Scientific Research     Open Access  
Journal of Symbolic Computation     Hybrid Journal   (Followers: 1)
Journal of the Australian Mathematical Society     Full-text available via subscription  
Journal of the Egyptian Mathematical Society     Open Access  
Journal of the European Mathematical Society     Full-text available via subscription   (Followers: 1)
Journal of the Indian Mathematical Society     Hybrid Journal   (Followers: 1)
Journal of the Institute of Mathematics of Jussieu     Hybrid Journal  
Journal of the London Mathematical Society     Hybrid Journal   (Followers: 2)
Journal of the Nigerian Mathematical Society     Open Access   (Followers: 1)
Journal of Theoretical and Applied Physics     Open Access   (Followers: 8)
Journal of Topology and Analysis     Hybrid Journal  
Journal of Transport and Supply Chain Management     Open Access   (Followers: 15)
Journal of Turbulence     Hybrid Journal   (Followers: 8)
Journal of Uncertainty Analysis and Applications     Open Access  
Journal of Universal Mathematics     Open Access  
Journal of Urban Regeneration & Renewal     Full-text available via subscription   (Followers: 11)
Journal of Water and Land Development     Open Access   (Followers: 3)
JRAMathEdu : Journal of Research and Advances in Mathematics Education     Open Access   (Followers: 4)
JUMLAHKU : Jurnal Matematika Ilmiah STKIP Muhammadiyah Kuningan     Open Access   (Followers: 5)
JURING (Journal for Research in Mathematics Learning)     Open Access   (Followers: 1)
Jurnal Ilmiah AdMathEdu     Open Access  
Jurnal Matematika     Open Access   (Followers: 1)
Jurnal Matematika Integratif     Open Access  
Jurnal Matematika, Sains, Dan Teknologi     Open Access  
Jurnal Natural     Open Access  
Jurnal Pendidikan Matematika Raflesia     Open Access  
Jurnal Penelitian Pembelajaran Matematika Sekolah     Open Access  
Jurnal Penelitian Sains (JPS)     Open Access  
Jurnal Riset Pendidikan Matematika     Open Access  
Jurnal Sains Matematika dan Statistika     Open Access  
Jurnal Tadris Matematika     Open Access  
Jurnal Teknologi dan Sistem Komputer     Open Access  
Kontinu : Jurnal Penelitian Didaktik Matematika     Open Access   (Followers: 3)
Kreano, Jurnal Matematika Kreatif-Inovatif     Open Access   (Followers: 5)
Le Matematiche     Open Access  
Learning and Teaching Mathematics     Full-text available via subscription   (Followers: 7)
Lettera Matematica     Hybrid Journal  
Lietuvos Matematikos Rinkinys     Open Access   (Followers: 3)
Limits : Journal of Mathematics and Its Applications     Open Access   (Followers: 1)
Linear Algebra and its Applications     Full-text available via subscription   (Followers: 23)
Linear and Multilinear Algebra     Hybrid Journal   (Followers: 8)
Lithuanian Mathematical Journal     Hybrid Journal  
LMS Journal of Computation and Mathematics     Free  
Lobachevskii Journal of Mathematics     Open Access  
Logic and Analysis     Hybrid Journal  
Logic Journal of the IGPL     Hybrid Journal  
Logica Universalis     Hybrid Journal  
manuscripta mathematica     Hybrid Journal  
MaPan : Jurnal Matematika dan Pembelajaran     Open Access  
Marine Genomics     Hybrid Journal   (Followers: 2)
Matemáticas, Educación y Sociedad     Open Access  
Matematicheskie Zametki     Full-text available via subscription  
Matematika     Open Access  
Matematychni Studii     Open Access  
Mathematica Eterna     Open Access  
Mathematica Scandinavica     Full-text available via subscription   (Followers: 1)
Mathematica Slovaca     Hybrid Journal   (Followers: 1)
Mathematical and Computational Forestry & Natural-Resource Sciences     Free  
Mathematical Communications     Open Access  
Mathematical Computation     Open Access   (Followers: 1)
Mathematical Geosciences     Hybrid Journal   (Followers: 3)
Mathematical Medicine and Biology: A Journal of the IMA     Hybrid Journal   (Followers: 1)
Mathematical Methods in the Applied Sciences     Hybrid Journal   (Followers: 4)
Mathematical Methods of Statistics     Hybrid Journal   (Followers: 4)
Mathematical Modelling and Analysis     Open Access   (Followers: 1)
Mathematical Modelling in Civil Engineering     Open Access   (Followers: 5)
Mathematical Modelling of Natural Phenomena     Full-text available via subscription   (Followers: 1)
Mathematical Models and Methods in Applied Sciences     Hybrid Journal   (Followers: 2)
Mathematical Models in Engineering     Open Access   (Followers: 2)
Mathematical Notes     Hybrid Journal  
Mathematical Proceedings of the Cambridge Philosophical Society     Full-text available via subscription   (Followers: 2)
Mathematical Programming Computation     Hybrid Journal   (Followers: 3)
Mathematical Sciences     Open Access  
Mathematical Social Sciences     Hybrid Journal   (Followers: 1)
Mathematical Theory and Modeling     Open Access   (Followers: 13)
Mathematical Thinking and Learning     Hybrid Journal   (Followers: 3)
Mathematics and Statistics     Open Access   (Followers: 5)
Mathematics Education Forum Chitwan     Open Access   (Followers: 1)
Mathematics Education Journal     Open Access   (Followers: 1)
Mathematics Education Research Journal     Partially Free   (Followers: 17)
Mathematics in Science and Engineering     Full-text available via subscription  
Mathematics of Control, Signals, and Systems (MCSS)     Hybrid Journal   (Followers: 5)
Mathematics of Quantum and Nano Technologies     Open Access  
Mathématiques et sciences humaines     Open Access   (Followers: 7)
Mathematische Annalen     Hybrid Journal   (Followers: 1)
Mathematische Nachrichten     Hybrid Journal   (Followers: 1)
Mathematische Semesterberichte     Hybrid Journal  
Mathematische Zeitschrift     Hybrid Journal   (Followers: 1)
MATI : Mathematical Aspects of Topological Indeces     Open Access  
MATICS     Open Access   (Followers: 2)
Matrix Science Mathematic     Open Access   (Followers: 1)
Measurement Science Review     Open Access   (Followers: 3)
Mediterranean Journal of Mathematics     Hybrid Journal  
Memetic Computing     Hybrid Journal  
Mendel : Soft Computing Journal     Open Access  
Metaheuristics     Hybrid Journal  
Metals and Materials International     Hybrid Journal  
Metascience     Hybrid Journal   (Followers: 1)
Milan Journal of Mathematics     Hybrid Journal  
Mitteilungen der DMV     Hybrid Journal  
MLQ- Mathematical Logic Quarterly     Hybrid Journal  
MONA : Matematik- og Naturfagsdidaktik     Hybrid Journal   (Followers: 3)
Monatshefte fur Mathematik     Hybrid Journal  
Moroccan Journal of Pure and Applied Analysis     Open Access   (Followers: 4)
Moscow University Mathematics Bulletin     Hybrid Journal  
MSOR Connections     Open Access   (Followers: 1)
Multiscale Modeling and Simulation     Hybrid Journal   (Followers: 3)
MUST : Journal of Mathematics Education, Science and Technology     Open Access   (Followers: 1)
Nagoya Mathematical Journal     Hybrid Journal  
Nano Research     Hybrid Journal   (Followers: 4)
Nanotechnologies in Russia     Hybrid Journal   (Followers: 1)
Natural Resource Modeling     Hybrid Journal   (Followers: 1)
New Mathematics and Natural Computation     Hybrid Journal  
Nonlinear Analysis : Modelling and Control     Open Access   (Followers: 1)
Nonlinear Analysis : Theory, Methods & Applications     Hybrid Journal   (Followers: 1)
Nonlinear Analysis: Hybrid Systems     Hybrid Journal  
Nonlinear Analysis: Real World Applications     Hybrid Journal   (Followers: 2)
Nonlinear Differential Equations and Applications NoDEA     Hybrid Journal  
Nonlinear Engineering     Open Access  
Nonlinear Oscillations     Hybrid Journal   (Followers: 1)
North Carolina Journal of Mathematics and Statistics     Open Access  
North-Holland Mathematical Library     Full-text available via subscription   (Followers: 1)

  First | 1 2 3 4 5     

Similar Journals
Journal Cover
Numerical Analysis and Applications
Journal Prestige (SJR): 0.164
Number of Followers: 1  
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1995-4247 - ISSN (Online) 1995-4239
Published by Springer-Verlag Homepage  [2626 journals]
  • Erratum to: Classification of Difference Schemes of Maximum Possible
           Accuracy on Extended Symmetric Stencils for the Schrödinger Equation and
           the Heat Conduction Equation
    • Abstract: Erratum
      PubDate: 2020-06-01
  • Calculation of Heat-Conducting Vapor–Gas–Drop Mixture Flows
    • Abstract: ABSTRACT A characteristic analysis of the equations of a single-velocity heat-conducting vapor–gas–drop mixture with interfractional heat transfer is carried out. The equations are shown to be hyperbolic. Calculation formulas for a Godunov-type method with a linearized Riemann solver are presented. These formulas are used to calculate some mixture flows.
      PubDate: 2020-06-01
  • Source Identification for the Smoluchowski Equation Using an Ensemble of
           Adjoint Equation Solutions
    • Abstract: ABSTRACT A source identification algorithm for systems of nonlinear ordinary differential equations of production-destruction type is applied to an inverse problem for a discretized Smoluchowski equation. An unknown source function is estimated by time series of measurements of particle concentrations of a specific size. Based on an ensemble of adjoint equation solutions, a sensitivity operator is constructed that relates perturbations of the sought-for model parameters with perturbations of the measured values. This reduces the inverse problem to a family of quasilinear operator equations. To solve the equations, an algorithm of the Newton–Kantorovich type with \(r\) -pseudoinverse matrices is used. The efficiency and properties of the algorithm are studied numerically.
      PubDate: 2020-06-01
  • Minimization Problem for Sum of Weighted Convolution Differences: The Case
           of a Given Number of Elements in the Sum
    • Abstract: ABSTRACT We consider an unstudied optimization problem of summing elements of two numerical sequences: \(Y\) of length \(N\) and \(U\) of length \(q\leq N\) . The objective of the problem is minimization of the sum of differences of weighted convolutions of sequences of variable length (not less than \(q\) ). In each difference, the first unweighted convolution is the autoconvolution of the sequence \(U\) expanded to a variable length due to multiple repetitions of its elements, and the second one is the weighted convolution of the expanded sequence with a subsequence from \(Y\) . We analyze a variant of the problem with a given input number of differences. We show that the problem is equivalent to that of approximation of the sequence \(Y\) by an element \(X\) of some exponentially-sized set of sequences. Such a set consists of all the sequences of length \(N\) that include as subsequences a given number \(M\) of admissible quasi-periodic (fluctuating) repetitions of the sequence \(U\) . Each quasi-periodic repetition results from the following admissible transformations of the sequence \(U\) : (1) shift of \(U\) by a variable, which do not exceed \(T_{\max}\leq N\) for neighboring repetitions, (2) variable expanding mapping of \(U\) to a variable-length sequence: variable-multiplicity repetitions of elements of \(U\) . The approximation criterion is minimization of the sum of the squares of element-wise differences. We demonstrate that the optimization problem and the respective approximation problem are solvable in a polynomial time. Specifically, we show that there exists an exact algorithm that solves the problem in the time \(\mathcal{O} (T_{\max}^{3}MN)\) . If \(T_{\max}\) is a fixed parameter of the problem, then the time taken by the algorithm is \(\mathcal{O} (MN)\) . In examples of numerical modeling, we show the applicability of the algorithm to solving model applied problems of noise-robust processing of electrocardiogram (ECG)-like and photoplethysmogram (PPG)-like signals.
      PubDate: 2020-06-01
  • A Low-Dissipation Numerical Scheme Based on a Piecewise Parabolic Method
           on a Local Stencil for Mathematical Modeling of Relativistic Hydrodynamic
    • Abstract: ABSTRACT A low-dissipation numerical method based on a combination of Godunov’s method and a piecewise parabolic method on a local stencil is presented. The construction of the method is described in detail. The method is tested using a one-dimensional problem of breakdown of a discontinuity. The results of a numerical simulation of collision of two relativistic gas spheres are given.
      PubDate: 2020-06-01
  • On Reducing an Inverse Boundary-Value Problem to the Synthesis of Two
           Ill-Posed Problems and Their Solution
    • Abstract: ABSTRACT An inverse boundary-value problem for the heat conduction equation is solved, and the error of the approximate solution is estimated. The Fourier transform with respect to time, which allows one to obtain an error estimate, is not applicable to the problem to be solved. Therefore, the variable in the heat conduction equation is replaced, resulting in the synthesis of problems and obtaining the estimate.
      PubDate: 2020-06-01
  • A Family of Solutions to the Two-Dimensional Eikonal Equation
    • Abstract: ABSTRACT The propagation of a wave from a point source when the velocity \(v\) in the medium is expressed as \(v = \frac {1}{\sqrt y}\) is considered. Exact solutions to the corresponding eikonal equation are obtained and numerically verified. It is shown that the solution of this equation when the point source is at the origin of coordinates is not unique.
      PubDate: 2020-06-01
  • Finite Element Method for the Stokes–Darcy Problem with a New
           Boundary Condition
    • Abstract: ABSTRACT This paper considers numerical methods for approximating and simulating the Stokes–Darcy problem, with a new boundary condition. We study a robust stabilized fully mixed discretization technique. This method ensures stability of the finite element scheme and does not use any Lagrange multipliers to introduce a stabilization term in the temporal Stokes–Darcy problem discretization. A correct finite element scheme is obtained and its convergence analysis is done. Finally, the efficiency and accuracy of these numerical methods are illustrated by different numerical tests.
      PubDate: 2020-06-01
  • Numerical Solution of the Direct Zakharov–Shabat Scattering Problem
    • Abstract: ABSTRACT A numerical solution of the direct scattering problem for the system of Zakharov–Shabat equations is considered. Based on the Marchuk identity, a method of fourth-order approximation accuracy is proposed. A numerical simulation of the scattering problem is made using two characteristic boundary value problems with known solutions as an example. The calculations have shown that the algorithm has high accuracy, which is necessary in many practical applications of optical and acoustic sensing in applied optics and geophysics.
      PubDate: 2020-06-01
  • An Efficient Parallel Implementation of the SIMPLE Algorithm Based on a
           Multigrid Method
    • Abstract: ABSTRACT This paper deals with a parallel implementation of the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm to numerically solve the Navier–Stokes system of equations for viscous incompressible flows. A mechanism of interprocess communication using a mesh decomposition with virtual cells and an algebraic multigrid method is proposed. A method of distributed matrix storage and an algorithm for matrix-vector operations reducing the number of interprocess communications are presented. The results of a series of numerical experiments on structured and unstructured grids (including a problem of external aerodynamics) are presented. Based on the results obtained, an analysis of the influence of multigrid solver settings on the overall efficiency of the algorithm is made. It is shown that the parallel algorithm based on an algebraic multigrid technique proposed for the SIMPLE method makes it possible to efficiently calculate problems on hundreds of processors.
      PubDate: 2020-02-01
  • Fourth-Order Numerical Scheme Based on Half-Step Non-Polynomial Spline
           Approximations for 1D Quasi-Linear Parabolic Equations
    • Abstract: ABSTRACT In this article, we discuss a fourth-order accurate scheme based on non-polynomial splines in tension approximations for solving quasi-linear parabolic partial differential equations (PDEs). The proposed numerical method requires only two half-step points and a central point on a uniform mesh in spatial direction. This method is derived directly from the continuity condition for the first-order derivative of the non-polynomial tension spline function. The stability of the scheme is discussed using a model linear PDE. The method is applicable for solving singular parabolic problems in polar systems. The proposed method is tested on the generalized Burgers–Huxley equation, generalized Burgers–Fisher equation, and Burgers’ equations in polar coordinates.
      PubDate: 2020-02-01
  • A Priori Error Estimates and Superconvergence of Splitting Positive
           Definite Mixed Finite Element Methods for Pseudo-Hyperbolic
           Integro-Differential Optimal Control Problems
    • Abstract: ABSTRACT In this paper we discuss a priori error estimates and superconvergence of splitting positive definite mixed finite element methods for optimal control problems governed by pseudo-hyperbolic integro-differential equations. The state variables and co-state variables are approximated by the lowest order Raviart–Thomas mixed finite element functions, and the control variable is approximated by piecewise constant functions. First, we derive a priori error estimates for the control variable, state variables, and co-state variables. Second, we obtain a superconvergence result for the control variable.
      PubDate: 2020-02-01
  • Classification of Difference Schemes of Maximum Possible Accuracy on
           Extended Symmetric Stencils for the Schrödinger Equation and the Heat
           Conduction Equation
    • Abstract: ABSTRACT All possible symmetric two-level difference schemes on arbitrary extended stencils are considered for the Schrödinger equation and for the heat conduction equation. The coefficients of the schemes are found from conditions under which the maximum possible order of approximation with respect to the main variable is attained. A class of absolutely stable schemes is considered in a set of maximally exact schemes. To investigate the stability of the schemes, the von Neumann criterion is verified numerically and analytically. It is proved that the schemes are absolutely stable or unstable depending on the order of approximation with respect to the evolution variable. As a result of the classification, absolutely stable schemes up to the tenth order of accuracy with respect to the main variable have been constructed.
      PubDate: 2020-02-01
  • Schemes of (m, k) -Type for Solving Differential-Algebraic and Stiff
    • Abstract: ABSTRACT A form of Rosenbrock-type methods optimal in terms of the number of non-zero parameters and computational costs per step is considered. A technique of obtaining \((m, k)\)-methods from some well-known Rosenbrock-type methods is justified. Formulas for transforming the parameters of \((m,k)\)-schemes and for obtaining a stability function are given for two canonical representations of the schemes. An \(L\)-stable \((3, 2)\)-method of order 3 is proposed, which requires two evaluations of the function: one evaluation of the Jacobian matrix and one \(LU\)-decomposition per step. A variable step size integration algorithm based on the \((3,2)\)-method is formulated. It provides a numerical solution for both explicit and implicit systems of ODEs. Numerical results are presented to show the efficiency of the new algorithm.
      PubDate: 2020-02-01
  • A Finite-Difference Scheme for the One-Dimensional Maxwell Equations
    • Abstract: ABSTRACT This paper deals with a difference scheme of second-order approximation using Laquerre transform for the one-dimensional Maxwell equations. Supplementary parameters are introduced into this difference scheme. These parameters are obtained by minimizing the error of a difference approximation for a Helmholtz equation. The optimal parameters do not depend on the step size and the number of nodes in the difference scheme. It is shown that the use of the Laguerre decomposition method allows obtaining higher accuracy of approximation of the equations in comparison with similar difference schemes when using the Fourier decomposition method. The second-order finite difference scheme with the parameters is compared to a fourth-order difference scheme in two cases: The use of the optimal difference scheme when solving a problem of electromagnetic pulse propagation in an inhomogeneous medium yields a solution accuracy comparable to that obtained with the fourth-order difference scheme. When solving an inverse problem the second-order difference scheme allows obtaining higher solution accuracy as compared to the fourth-order difference scheme. In these problems the second-order difference scheme with the supplementary parameters has decreased the calculation time by 20–25% as compared to the fourth-order difference scheme.
      PubDate: 2020-02-01
  • Convergence of Numerical Spectral Models of Sea Surface Undulations
    • Abstract: ABSTRACT This paper deals with convergence of spectral and conditional spectral models to simulate the stochastic structure of sea surface undulations and rogue ocean waves. Convergence of spatial-temporal and spatial models is studied in particular.
      PubDate: 2020-02-01
  • Numerical Solution of a Three-Dimensional Coefficient Inverse Problem for
           the Wave Equation with Integral Data in a Cylindrical Domain
    • Abstract: Abstract A three-dimensional coefficient inverse problem for the wave equation (with losses) in a cylindrical domain is considered. The data given for its solution are special time integrals of a wave field measured in a cylindrical layer. We present and substantiate an efficient algorithm for solving this three-dimensional problem based on the fast Fourier transform. The algorithm makes it possible to obtain a solution on 512× 512×512 grids in about 1.4 hours on a typical PC without paralleling the calculations. The results of numerical experiments of model inverse problem solving are presented.
      PubDate: 2019-10-01
  • Improving the Stability of Triangular Decomposition of Ill-Conditioned
    • Abstract: Abstract An approach to improving the stability of triangular decomposition of a dense positive definite matrix with a large condition number by using the Gauss and Cholesky methods is considered. It is proposed to introduce additions to standard computational schemes with an incomplete inner product of two vectors which is formed by truncating the lower digits of the sum of the products of two numbers. The truncation in the process of decomposition increases the diagonal elements of the triangular matrices by a random number and prevents the appearance of very small numbers during the Gauss decomposition and a negative radical expression in the Cholesky method. The number of additional operations required for obtaining an exact solution is estimated. The results of computational experiments are presented.
      PubDate: 2019-10-01
  • Numerical Method for Predicting Hemodynamic Effects in Vascular Prostheses
    • Abstract: Abstract A three-dimensional unsteady periodic flow of blood in xenogenic vascular bioprostheses is simulated by computational fluid dynamics methods. The geometry of the computational domain is based on microtomographic scanning of bioprostheses. To set a variable pressure gradient causing an unsteady flow in the prostheses, personal-specific data of the Doppler echography of the blood flow of a particular patient are used. A comparative analysis of the velocity fields in the flow areas corresponding to three real samples of bioprostheses with multiple stenoses is carried out. In the zones of stenosis and outside of them, the distribution of the near-wall shear stress, which affects the risk factors for thrombosis in the prostheses, is analyzed. An algorithm for predicting the hemodynamic effects arising in vascular bioprostheses is proposed; the algorithm is based on the numerical modeling of the blood flow in these prostheses.
      PubDate: 2019-10-01
  • Conservation Laws and Other Formulas for Families of Rays and Wavefronts
           and for the Eikonal Equation
    • Abstract: Abstract In the previous studies, the author has obtained conservation laws for the 2D eikonal equation in an inhomogeneous isotropic medium. These laws are divergent identities of the form div F = 0. The vector field F is expressed through a solution to the eikonal equation (the time field), the refractive index (the equation parameter), and their partial derivatives. Besides that, equivalent conservation laws (divergent identities) were found for families of rays and families of wavefronts in terms of their geometric characteristics. Thus, the geometric essence (interpretation) of the conservation laws obtained for the 2D eikonal equation was found. In this paper, 3D analogs of the results obtained are presented: differential conservation laws for the 3D eikonal equation and conservation laws (divergent identities of the form div F = 0) for families of rays and families of wavefronts, the vector field F expressed through classical geometric characteristics of the ray curves: their Frenet basis (the unit tangent vector, principal normal, and binormal), the first curvature, and the second curvature, or through the classical geometric characteristics of the wavefront surfaces: their normal, principal directions, principal curvatures, Gaussian curvature, and mean curvature. All the results have been obtained on the basis of the general vector and geometric formulas (differential conservation laws and some formulas) obtained for families of arbitrary smooth curves, families of arbitrary smooth surfaces, and arbitrary smooth vector fields.
      PubDate: 2019-10-01
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh, EH14 4AS, UK
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