Lotova, G. Z. Mikhailov, G. A.
Published in
Computational Mathematics and Mathematical Physics

It is well known that, under rather general conditions, the particle flux density in a multiplying medium is asymptotically exponential in time \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-...

Kuznetsov, D. F.
Published in
Computational Mathematics and Mathematical Physics

AbstractThis paper is devoted to the development and application of the Fourier method to the numerical solution of Ito stochastic differential equations. Fourier series are widely used in various fields of applied mathematics and physics. However, the method of Fourier series as applied to the numerical solution of stochastic differential equation...

Shananin, A. A. Tarasenko, M. V. Trusov, N. V.
Published in
Computational Mathematics and Mathematical Physics

AbstractAn optimal control problem modeling the economic behavior of a representative household is studied. The existence of its solution is proved, necessary optimality conditions in the form of the Pontryagin–Clarke maximum principle are obtained, and an optimal control synthesis is constructed. The model is identified against Russian statistical...

Kuznetsov, D. F.
Published in
Computational Mathematics and Mathematical Physics

AbstractThis paper is devoted to the comparative analysis of the efficiency of using the Legendre polynomials and trigonometric functions for the numerical solution of Ito stochastic differential equations under the method of approximating multiple Ito and Stratonovich stochastic integrals based on generalized multiple Fourier series. Using the mul...

Yang, Qian Ni, Mingkang
Published in
Computational Mathematics and Mathematical Physics

AbstractThis paper investigates a two-point boundary value problem for a second-order singularly perturbed ordinary differential equation in the case of multiple roots of the degenerate equation. This is a new class of problems, namely, problems with discontinuous nonlinear terms on the right-hand side of the equation, which leads to the formation ...

Varin, V. P.
Published in
Computational Mathematics and Mathematical Physics

AbstractWe consider the problem of interpolation of recurrent functions given at integer points. Interpolation is understood as a construction of an analytic function that takes given values at given points. In a special case of iterations of analytic functions, i.e., of composition of analytic maps, this is a classical problem of construction of c...

Otelbaev, M. Soldatov, A. P.
Published in
Computational Mathematics and Mathematical Physics

AbstractGeneralized integrals are introduced with kernels depending on the difference of the arguments taken over a domain and a smooth contour, the boundary of this domain. These kernels arise as parametrixes of first-order elliptic systems with variable coefficients. Using such integrals (with complex density over the domain and real density over...

Matevossian, H. A.
Published in
Computational Mathematics and Mathematical Physics

AbstractThe uniqueness of solutions of a biharmonic problem with Dirichlet and Steklov-type boundary conditions in the exterior of a compact set are studied under the assumption that the generalized solution of this problem has a finite Dirichlet integral with a weight \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepack...

Bakhshaliyeva, M. N. Khalilov, E. H.
Published in
Computational Mathematics and Mathematical Physics

AbstractA curvilinear integral equation of the exterior Dirichlet boundary value problem for the Laplace equation is considered. A new method is proposed to construct a quadrature formula for a singular integral. The method is used to derive a quadrature formula for the normal derivative of the double layer logarithmic potential. For specifically c...

Voloshchenko, A. M.
Published in
Computational Mathematics and Mathematical Physics

AbstractA \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K{{P}_{1}}$$\end{document} scheme for accelerating the convergence of inner iterations is constructed for the ...