Troshkin, O. V.
Published in
Computational Mathematics and Mathematical Physics

AbstractThe dynamics of a continuous medium in a pipe is not exhausted by spontaneous unsteady turbulence vortices (first seen in flashes of light and generated at high Reynolds numbers), which permanently level the parabolic velocity profile in the pipe. The ambient space also includes steady swirls and curls, which are usually approximated by ana...

Mardanov, R. F. Mardanova, A. E.
Published in
Computational Mathematics and Mathematical Physics

AbstractA boundary element method is proposed for solving an inhomogeneous biharmonic equation with a right-hand side containing the sought function and its derivatives. The accuracy of numerical results obtained for a test problem is analyzed by comparing them with its analytical solution. The flow through a porous medium with a nonuniform permeab...

Bulatov, V. V. Vladimirov, Yu. V.
Published in
Computational Mathematics and Mathematical Physics

AbstractThe problem of constructing analytical solutions describing internal gravity wave fields generated by a nonlocal source of perturbations moving on the surface of a stratified medium of finite depth is considered. For a radially symmetric model source, analytical solutions expressed in terms of eigenfunctions of the basic vertical spectral p...

Zarafutdinov, I. A. Pityuk, Yu. A. Solnyshkina, O. A.
Published in
Computational Mathematics and Mathematical Physics

AbstractAn efficient numerical approach to the study of the dynamics of a cluster containing bubbles and solid particles under the action of an acoustic field in the 3D case is presented. The numerical method is a combination of the boundary element method (BEM) and the fast multipole method (FMM) for the Laplace equation. The hardware acceleration...

Kvitko, A. N.
Published in
Computational Mathematics and Mathematical Physics

AbstractAn algorithm, quite convenient for numerical implementation, is proposed for constructing a differentiable control function that guarantees the transfer of a wide class of nonlinear stationary systems of ordinary differential equations from the initial state to a given final state of the phase space, taking into account control constraints ...

Krukovskii, A. Yu. Poveshchenko, Yu. A. Podryga, V. O. Rahimly, P. I.
Published in
Computational Mathematics and Mathematical Physics

AbstractA finite-difference approximation of elastic forces on Lagrangian grids is constructed by applying the support operator method. For displacement vectors on unstructured grids with minimal reasonable constraints imposed on their topological and geometric structure, approximations of vector analysis operations are constructed as applied to di...

Abdullayev, V. M. Aida-zade, K. R.
Published in
Computational Mathematics and Mathematical Physics

AbstractThe problem of optimizing the right-hand sides of linear nonlocal multipoint conditions for a linear system of differential equations is considered. Necessary optimality conditions of the first order are obtained, which allow the use of efficient first-order methods for the numerical solution of the problem under consideration. Solutions of...

Eremin, Yu. A. Sveshnikov, A. G.
Published in
Computational Mathematics and Mathematical Physics

AbstractWorks concerning the quantum effect of nonlocal screening on field characteristics in the problem of scattering a plane wave by nanoscale structures, including ones located near a transparent substrate, are reviewed. Efficient computer models for analyzing such structures are constructed by applying the discrete source method. The nonlocali...

Yukhno, L. F.
Published in
Computational Mathematics and Mathematical Physics

AbstractFor an algebraic spectral problem that is linear with respect to the spectral parameter, some numerical methods are considered to find the root space corresponding to a chosen eigenvalue. These methods make it possible to construct the root space as a whole without calculating the corresponding eigenvectors and associated vectors. The propo...

Bragin, M. D. Rogov, B. V.
Published in
Computational Mathematics and Mathematical Physics

AbstractBicompact schemes are generalized for the first time to the linear multidimensional convection–diffusion equation. Schemes are constructed using the method of lines, the finite-volume method, and bi- and tricubic Hermite interpolation of the sought function in a cell. Time stepping is based on diagonally implicit Runge–Kutta methods. The pr...