Asan ÖMÜRALİEV | Ella ABILAYEVA

Article | 2022 | Journal of Mathematical Sciences264 ( 4 )

In this paper we construct the asymptotics of the solution of the Cauchy problem for a singularly perturbed hyperbolic system by using the regularization method for singularly perturbed problems of S.A. Lomov. The regularization method for singularly perturbed problems of S.A. Lomov is used for the first time to construct the asymptotic solution of a hyperbolic system.

Dağıstan ŞİMŞEK | Fahreddin ABDULLAYEV

Article | 2017 | Journal of Mathematical Sciences222 ( 6 )

The solution of the difference equation (Formula presented.),..., where x−(4k+3), x−(4k+2),..., x−1, x0 ∈ (0, ∞) and k = 0, 1,..., is studied.

Meerim İmaş Kızı | Fahreddin ABDULLAYEV

Article | 2018 | Journal of Mathematical Sciences234 ( 1 )

We have obtained the pointwise Bernstein–Walsh type estimation for algebraic polynomials in the unbounded regions with piecewise asymptotically conformal boundary, having exterior and interior zero angles, in the weighted Lebesgue space.

Asan ÖMÜRALİEV

Article | 2018 | Journal of Mathematical Sciences230 ( 5 )

We examine a system of singularly perturbed parabolic equations in the case where the small parameter is involved as a coefficient of both time and spatial derivatives and the spectrum of the limit operator has a multiple zero point. In such problems, corner boundary layers appear, which can be described by products of exponential and parabolic boundary-layer functions. Under the assumption that the limit operator is a simple-structure operator, we construct a regularized asymptotics of a solution, which, in addition to corner boundary-layer functions, contains exponential and parabolic boudary-layer functions. The construction of t . . .he asymptotics is based on the regularization method for singularly perturbed problems developed by S. A. Lomov and adapted to singularly perturbed parabolic equations with two viscous boundaries by A. S. Omuraliev More less

Avıt ASANOV | Kalıskan MATANOVA

Article | 2022 | Journal of Mathematical Sciences262 ( 2 )

A numerical solution of the system of linear Volterra–Stieltjes integral equations of the second kind has been found and analyzed using the so-called generalized trapezoid rule. Conditions for estimating the error have also been determined and justified. A solution of an example obtained using the proposed method is given.

Asan ÖMÜRALİEV | Ella ABILAYEVA

Article | 2019 | Journal of Mathematical Sciences242 ( 3 )

The regularized asymptotics of a solution of the Cauchy problem for systems of singularly perturbed ordinary differential equations is constructed. It is shown that a power boundary layer appears in such problems in addition to other boundary layers.

Dağıstan ŞİMŞEK

Article | 2018 | Journal of Mathematical Sciences234 ( 1 )

A solution of the following difference equation is investigated:xn+1=xn−(k+1)1+xnxn−1…xn−k,n=0,1,2,… where x−(k+1); x−k; : : : ; x−1; x0 𝜖 (0;∞) and k = 0; 1; 2; : : :.