Published in Computational Mathematics and Mathematical Physics
AbstractComplex matrices having \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{J}_{n}}(1)$$\end{document} as the cosquare are shown to be nonsingular matrices \docum...
Published in Computational Mathematics and Mathematical Physics
AbstractThe dissipation and dispersion properties of the Hermite characteristic scheme intended for solving the one-dimensional advection equation are examined. The scheme is based on Hermite interpolation using not only the nodal values of the function, but also the nodal values of its spatial derivative. The derivatives at a new time step are com...
Published in Computational Mathematics and Mathematical Physics
AbstractThe article presents the construction of k-step methods for solving systems of Volterra integral equations of the first and the second kind with a weak power-law singularity of the kernels in the lower limit of integration. The matrix-vector representation of such systems has the form of an abstract equation with a degenerate coefficient ma...
Published in Computational Mathematics and Mathematical Physics
AbstractNew high-order nonlinear equations of the Sobolev type describing ion-sound plasma waves in an external electric or magnetic field are derived. Despite the cumbersome form of the equations, research techniques are developed for corresponding initial and initial-boundary value problems. Specifically, based on the present results, sufficient ...
Published in Computational Mathematics and Mathematical Physics
AbstractThe paper is devoted to the statement of the beamforming problem the goal of which is the determination of the continuous acoustic source function based on the analysis of time–space data obtained in computational experiments in aerodynamics and aeroacoustics problems. Here the computational experiment is a highly accurate reproduction of t...
Published in Computational Mathematics and Mathematical Physics
AbstractThis work continues previous studies of the authors and provides an analytical solution to the plane problem of symmetric cavitating flow of an ideal fluid over a wedge for Tulin’s cavity closure model with a double-spiral vortex. The solution is expressed in terms of the Lauricella hypergeometric function. A numerical implementation of the...
Published in Computational Mathematics and Mathematical Physics
AbstractThe problem of minimizing a function with a Lipschitz continuous gradient is considered on a proximally smooth subset that is a smooth manifold without boundary. The gradient projection method with Armijo’s step size is discussed, and its linear convergence is proved. An exact constant of proximal smoothness is obtained for various matrix s...
Published in Computational Mathematics and Mathematical Physics
AbstractAsymptotic analysis is used to study the existence, local uniqueness, and asymptotic Lyapunov stability of the solution to a one-dimensional nonlinear parabolic system of the activator–inhibitor type. A specific feature of the problem is the discontinuities of the first kind of the functions on the right-hand sides of the equations. The jum...
Published in Computational Mathematics and Mathematical Physics
AbstractA analytic review of major problems and new mathematical and technological discoveries in methods for solving SLAEs is given. This stage of mathematical modeling is a bottleneck because the amount of the required computational resources grows nonlinearly with the increasing number of degrees of freedom of the problem. It is important that t...
Published in Computational Mathematics and Mathematical Physics
AbstractThe model problem of heat transfer from a nonuniformly heated pipe wall to the basic flow is considered, or, in other words, the initial stages of fluid temperature and pressure relaxation in a heated pipe are addressed. The computations are based on computer codes using various combinations of the Navier–Stokes equations, a modified Burnet...
