Approximate solution of Wiener-Hopf integral equations and its discrete counterpartsPleiades Publishing Ltd - Tập 55 - Trang 834-843 - 2015
A. G. Barseghyan, N. B. Engibaryan
A method for averaging the kernel of a numerical-analytical solution of nonsingular Wiener-Hopf (WH) equations is proposed. By applying a discretization technique similar to the strip method, the WH integral equation is reduced to a discrete WH equation. A priori estimates are obtained that ensure the uniform convergence of the method. Two techniques for solving discrete WH equations are developed...... hiện toàn bộ
On Analytic Continuation of Conformal Mapping of a Circular TrianglePleiades Publishing Ltd - Tập 62 - Trang 2112-2122 - 2023
S. V. Pikulin
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...... hiện toàn bộ
Solution blow-up for a new stationary Sobolev-type equationPleiades Publishing Ltd - Tập 50 - Trang 831-847 - 2010
M. O. Korpusov, A. G. Sveshnikov
A new nonlinear stationary Sobolev-type equation with a parameter η ∈ ℝ1 is derived. For η > 0, global solvability in the weak generalized sense is proved in the entire waveguide
$$
\mathbb{S}
$$
⊗ ℝ
+
1
. For η < 0, the strong generalized solution is s...... hiện toàn bộ
Method of adaptive artificial viscosity for solving the Navier–Stokes equationsPleiades Publishing Ltd - Tập 55 - Trang 1324-1329 - 2015
I. V. Popov, I. V. Fryazinov
A numerical technique based on the method of adaptive artificial viscosity is proposed for solving the viscous compressible Navier–Stokes equations in two dimensions. The Navier–Stokes equations is approximated on unstructured meshes, namely, on triangular or tetrahedral elements. The monotonicity of the difference scheme according to the Friedrichs criterion is achieved by adding terms with adapt...... hiện toàn bộ
Numerical Solution of Test Problems Using a Modified Godunov SchemePleiades Publishing Ltd - Tập 58 - Trang 1573-1584 - 2018
Yu. V. Tunik
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...... hiện toàn bộ
Minimax algorithm for constructing an optimal control strategy in differential games with a Lipschitz payoffPleiades Publishing Ltd - Tập 51 - Trang 550-574 - 2011
G. E. Ivanov, V. A. Kazeev
For a zero-sum differential game, an algorithm is proposed for computing the value of the game and constructing optimal control strategies with the help of stepwise minimax. It is assumed that the dynamics can be nonlinear and the cost functional of the game is the sum of an integral term and a terminal payoff function that satisfies the Lipschitz condition but can be neither convex nor concave. T...... hiện toàn bộ
Solution of the self-adjoint radiative transfer equation on hybrid computer systemsPleiades Publishing Ltd - Tập 56 - Trang 987-995 - 2016
V. A. Gasilov, P. A. Kuchugov, O. G. Olkhovskaya, B. N. Chetverushkin
A new technique for simulating three-dimensional radiative energy transfer for the use in the software designed for the predictive simulation of plasma with high energy density on parallel computers is proposed. A highly scalable algorithm that takes into account the angular dependence of the radiation intensity and is free of the ray effect is developed based on the solution of a second-order equ...... hiện toàn bộ