Approximate Solution of the System of Linear Volterra-Stieltjes Integral Equations of the Second Kind

Avıt ASANOV | Kalıskan MATANOVA

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.

Выбор параметров решения линейных неклассических уравнений первого рода

Avıt ASANOV

В рассматриваемой работе выбран параметр регуляризации для решения линейного интегрального уравнения Вольтерра первого рода. Во многих работах были исследованы различные вопросы для интегральных уравнений. Даже когда уравнение первого типа Вольтерры является интегральным уравнением с точным выходом, неклассические уравнения, интегрируемые по предел, являются линейными, и нелинейные интегральные уравнения являются линейными, и это обусловлено необходимостью разработки новых методов для единственности их решений. Но в данной работе получены основополагающие результаты для интегральных уравнений ...More

Approximate Solution of the System of Linear Volterra-Stieltjes Integral Equations of the Second Kind

Avıt ASANOV | Kalıskan MATANOVA

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. Keyword: System of linear Volterra-Stieltjes integral equations, second kind, generalized trapezoid rule, numerical solution

Uniqueness and stability of solutions of linear intergral equations of the first kind with two variables

Avıt ASANOV | Mustafa Haluk ÇELİK

In this paper is dedicated to the research of the problem of uniqueness and stability of solutions for linear integral Equations of the first kind with two variables. Here the operator generated by the kernels is not the compact operator.

Uniqueness and Stability of Solutions for Certain Linear Equations of the First Kind With Two Variables = Единственность и устойчивость решений для некоторых интегральных уравнений первого рода с двумя независимыми переменными

Avıt ASANOV

The article is devoted to the study of uniqueness and stability of solutions of linear integral equations of the first kind with two independent variables. The relevance of the problem is due to the needs in development of new approaches for the regularization and uniqueness of the solution of linear integral equations of the first kind with two independent variables. Integral and operator equations of the first kind with two independent variables arise in theoretical and applied problems.Works of A.N. Tikhonov, M.M. Lavrentyev and B.K. Ivanov, in which a new concept of correctness of setting ...More

One Formula for Solution of the Linear Differential Equations of the Second Order with the Variable Coefficients

Avıt ASANOV | Mustafa Haluk ÇELİK

In this paper we obtained the formula for the common solution of the linear differential equation of the second order with the variable coefficients in the more common case. We also obtained the formula for the solution of the Cauchy problem. © Research India Publications.

A class linear integral equations of Fredholm-Stilties of the first kind = Об одном классе линейных интегральных уравнений Фредгольма-Стилтьеса первого рода

Avıt ASANOV

In this article the line.r integral equation of Fredgolm-Stilties of the first kind is given. Using the method proposed in A. Asanov, estimates and stability built on M.M.Lavrentev regularizing operator for solving singularly perturbed integral equations of the first kind. The questions of uniqueness of solution of the integral equation and prove a theorem about the sustainability assessment solutions in the classroom L-2.

A class of systems of linear Fredholm integral equations of the third kind

Avıt ASANOV

Об одном классе систем линейных интегральных уравнений Фредгольма третьего рода

Avıt ASANOV

Approximating the Stieltjes integral by using the generalized trapezoid rule

Avıt ASANOV | Mustafa Haluk ÇELİK

Accurate approximations for the Stieltjes integral by the generalized trapezoid rule. The generalized trapezoid rule is established on the basis of the derivative of function with respect to strictly increasing function, defined in [9].

Approximating the Stieltjes Integral Using the Generalized Midpoint Rule

Avıt ASANOV | Mustafa Haluk ÇELİK

Accurate approximations for the Stieltjes integral by the generalized midpoint rule. The generalized midpoint rule is established on the notion of the derivative of function with respect to the strictly increasing function defined in [9]. Keywords: Stieltjes integral; generalired midpoint rule; the derivative of the function with respect to the strictly increasing function; generalized formula of Taylor. 2010 Mathematics Subject Classification 26D15; 26A42.

Solutions to systems of linear Fredholm integral equations of the third kind

Avıt ASANOV