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On Analytic Continuation of Conformal Mapping of a Circular Triangle
Pleiades Publishing Ltd - Tập 62 - Trang 2112-2122 - 2023
Given a circular triangle T having a zero angle at a point at infinity and two equal nonzero angles, it is shown that a conformal mapping of T onto a half-plane can be continued to a semi-infinite strip by applying the Riemann–Schwarz symmetry principle. The problem of analytic continuation of such a mapping arises as an auxiliary problem in constructing a conformal mapping of an L-shaped domain o......
Numerical Solution of Test Problems Using a Modified Godunov Scheme
Pleiades Publishing Ltd - Tập 58 - Trang 1573-1584 - 2018
Modifications of Godunov’s scheme based on V.P. Kolgan’s approach to the construction of second-order accurate schemes in space for smooth solutions are proposed. The gasdynamic parameters linearly interpolated in a mesh cell, but the Riemann problem is solved for parameters at an intermediate point between the center and the boundary of the cell. Properties of Kolgan’s scheme and the proposed mod......
Modified Kantorovich theorem and asymptotic approximations of solutions to singularly perturbed systems of ordinary differential equations
Pleiades Publishing Ltd - Tập 56 - Trang 1859-1871 - 2016
The functional equation f(x,ε) = 0 containing a small parameter ε and admitting regular and singular degeneracy as ε → 0 is considered. By the methods of small parameter, a function x
n
0(ε) satisfying this equation within a residual error of O(ε
n+1) is found. A ......
On the Best Approximation Algorithm by Low-Rank Matrices in Chebyshev’s Norm
Pleiades Publishing Ltd - Tập 62 - Trang 701-718 - 2022
The problem of approximation by low-rank matrices is found everywhere in computational mathematics. Traditionally, this problem is solved in the spectral or Frobenius norm, where the approximation efficiency is associated with the rate of decrease of the matrix singular values. However, recent results show that this requirement is not necessary in other norms. In this paper, a method for solving t......
On one class of dynamic transportation models
Pleiades Publishing Ltd - Tập 53 - Trang 1466-1482 - 2013
A model is studied that describes the process of good transportation occurring in some technologies. Transportation regimes satisfying a given management system are examined. Such regimes are described by traveling-wave solutions to a nonlinear finite-difference analogue of a parabolic equation. Possible transportation regimes are described, and the stability of stationary regimes is analyzed.
Duality theory of optimal adaptive methods for polyhedral approximation of convex bodies
Pleiades Publishing Ltd - Tập 48 - Trang 376-394 - 2011
A duality theory is developed to describe iterative methods for polyhedral approximation of convex bodies. The various types of approximation problems requiring the application of the duality theory are considered. Based on the theory, approximation methods can be designed for bodies with a dual description (in terms of the support/distance function) and methods can be developed that are optimal i......
Analysis of Approximate Solution for a Class of Systems of Integral Equations
Pleiades Publishing Ltd - Tập 62 - Trang 811-826 - 2022
The paper presents a substantiation of the collocation method for a system of integral equations for the field-matching boundary value problem for the Helmholtz equation in two-dimensional space. Quadrature formulas are constructed for the single and double layer potentials and the normal derivative of the single layer potential. At definite points, the system of integral equations is replaced by ......
Influence of the Shock Wave Intensity on Instability Development at Rough Interfaces of a Three-Layer Gas System
Pleiades Publishing Ltd - Tập 63 - Trang 413-424 - 2023
The influence exerted by the intensity of a shock wave transmitted through rough interfaces on instability development in a three-layer gas system at Mach numbers M = 1.3 and M = 3 is studied. The three-layer system is obtained by placing two thin films (interfaces) across a shock tube. A heavy gas (sulfur hexafluoride) occupies the space between the interfaces (the central layer of the system), w......
Stationary Problem of Radiative Heat Transfer with Cauchy Boundary Conditions
Pleiades Publishing Ltd - - 2019
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