Journal of Applied and Industrial Mathematics最新文献

Abstract

The paper deals with the numerical solution of fractional differential equations withinterval parameters in terms of derivatives describing anomalous diffusion processes.Computational algorithms for solving initial–boundary value problems as well as thecorresponding inverse problems for equations containing interval fractional derivatives withrespect to time and space are presented. The algorithms are based on the previously developedand theoretically substantiated adaptive interpolation algorithm tested on a number of appliedproblems for modeling dynamical systems with interval parameters; this makes it possible toexplicitly obtain parametric sets of states of dynamical systems. The efficiency and workability ofthe proposed algorithms are demonstrated in several problems.

Abstract

Our objective is to calculate the derivatives of data corrupted by noise. This isa challenging task as even small amounts of noise can result in significant errors in thecomputation. This is mainly due to the randomness of the noise, which can result inhigh-frequency fluctuations. To overcome this challenge, we suggest an approach that involvesapproximating the data by eliminating high-frequency terms from the Fourier expansion of thegiven data with respect to the polynomial-exponential basis. This truncation method helps toregularize the issue, while the use of the polynomial-exponential basis ensures accuracy in thecomputation. We demonstrate the effectiveness of our approach through numerical examples inone and two dimensions.

Abstract

The paper studies the problem of determining the error introduced by inaccuracy indetermining the thickness of a protective heat-resistant coating of composite materials. Themathematical problem is the heat equation on an inhomogeneous half-line. The temperature onthe outer side of the half-line (( x=0 )) is considered unknown over an infinite time interval. To find it, thetemperature is measured at the interface of the media at the point( x=x_0 ). An analytical study of the direct problem is carried out and enables arigorous statement of the inverse problem and determining the functional spaces in which it isnatural to solve the inverse problem. The main difficulty that the present paper aims at solving isobtaining an estimate for the error of the approximate solution. To estimate the conditionalcorrectness modulus, the projection regularization method is used; this allows obtainingorder-accurate estimates.

Abstract

The Temetos platform is designed to conduct computational experiments at all stages ofanalysis and study of continuum mechanics models. A module has been developed to study thestress–strain state of a system of bodies with allowance for inelastic strains and contactinteraction. It was used to analyze a fuel element that included up to 100 fuel pellets and a shell.The platform’s solvers are applied to astrophysics problems. Models of the formation of accretiondisks in binary star systems that allow the interpretation of observation results are constructed.

Abstract

The paper provides an overview of the main approaches to the construction ofpost-quantum cryptographic systems that are currently used. The area of lattice-basedcryptography is analyzed in detail. We give the description and characterization of some knownlattice-based cryptosystems whose resilience is based on the complexity of the shortest vectorproblem, learning with errors problem, and their variations. The main approaches to solving theproblems from lattice theory, on which attacks on the corresponding cryptosystems are based, areanalyzed. In particular, some known theoretical estimates of time and memory complexity oflattice basis reduction and lattice sieving algorithms are presented.

Abstract

The Rusanov solver for solving hydrodynamic equations is one of the most robust schemesin the class of Riemann solvers. For special relativistic hydrodynamics, the robustness condition ofthe scheme is the most important property, especially for sufficiently high values of the Lorentzfactor. At the same time, the Rusanov solver is known to be very dissipative. It is proposed to usea piecewise parabolic representation of physical variables to reduce the dissipation of the Rusanovscheme. Using this approach has made it possible to obtain a scheme with the same dissipativeproperties as Roe-type schemes and the family of Harten–Lax–van Leer schemes. Using theproblem of the decay of a relativistic hydrodynamic discontinuity, it is shown that the presentauthor’s version of the Rusanov scheme is advantageous in terms of reproducing a contactdiscontinuity. The scheme is verified on classical problems of discontinuity decay and on theproblem of the interaction of two relativistic jets in the three-dimensional formulation.

Abstract

In this work, we study the influence of orientation on the stability conditions of thereaction front where the monomer is solid and the polymer is liquid. The mathematical modelincludes the heat equation, the concentration equation and the Navier–Stokes equation under theBoussinesq approximation. We use the method proposed by Zeldovich and Frank-Kamenetskii toperform asymptotic analysis. We then perform a stability analysis. The linearized problem issolved numerically using a multiquadric radial basis function method (MQ-RBF) to find thestability boundary. This will allow us to deduce the influence of each control parameter of theproblem on this stability, in particular the angle of inclination of the experimental tube.

Abstract

We consider the Navier–Stokes equations for the plane steady motion of a viscousincompressible fluid in an orthogonal coordinate system in which the fluid streamlines coincidewith the coordinate lines of one of the families of the orthogonal coordinate system. In thiscoordinate system, the velocity vector has only the tangential component and the system of threeNavier–Stokes equations is an overdetermined system for two functions—the tangentialcomponent of velocity and pressure. In the present paper, the system is brought to involution, andthe consistency conditions are obtained, which are the equations for the curl of the velocity in thiscoordinate system. The coefficients of these equations include the curvatures of the coordinatelines and their derivatives up to the second order. The equations obtained are significantly morecomplicated than the curl equations in a channel of simple geometry.

Abstract

The reconstruction of physical properties of a medium from boundary measurements,known as inverse scattering problems, presents significant challenges. The present study aims tovalidate a newly developed convexification method for a 3D coefficient inverse problem in the caseof buried unknown objects in a sandbox, using experimental data collected by a microwavescattering facility at The University of North Carolina at Charlotte. Our study considers theformulation of a coupled quasilinear elliptic system based on multiple frequencies. The system canbe solved by minimizing a weighted Tikhonov-like functional, which forms our convexificationmethod. Theoretical results related to the convexification are also revisited in this work.

We consider a competitive facility location model where competing parties (Leader andFollower) make decisions considering changes of the set of customers happening during the planinghorizon consisting a known number of time periods. It is assumed that the Leader makes adecision on opening their facilities at the beginning of the planning horizon, while the Follower canrevise their decision in each time period. In the present paper, we study perspectives to apply amethod for finding the best solution that is based on using HP-relaxation of the bilevel problemconsidered. The key element of this method is construction of additional inequalitiesstrengthening the HP-relaxation and computation of upper bounds for the objective function ofthe problem. In the paper, we propose new families of additional constraints to strengthen theHP-relaxation that allow computing nontrivial upper bounds.