One Class of Linear Fredholm Operator Equations of the Third Kind

Avıt ASANOV | Kalıskan MATANOVA

In this paper, we are applied a new approach to prove that the solution of the linear Fredholm operator equation of the third kind given on a segment and having a finite number of multipoint singularities is equivalent to the solution of the linear Fredholm operator equation of the second kind with additional conditions. We are showed an example of solving the system of linear integral Fredholm equations of the third kind based on the equivalence of the above equations.

On numerical solution of the second-order linear Fredholm-Stieltjes integral equation

Avıt ASANOV

In this framework, the necessary and sufficient conditions for the existence and uniqueness of the second-order linear Fredholm-Stieltjes-integral equations, u(x) = lambda integral(b)(a) K(x, y) u(y) dg(y) + f(x), x is an element of[a, b], are thoroughly derived. Moreover, instead of approximating the integral equation by different numbers of partition n, the optimal number n for the given error tolerance is established. The system of equations is implemented in MAPLE for the Runge method. An efficient scheme is proposed for second-order integral equations. The solution has been compared with ...Более

Задача восстановления ядра и правой части интегро-дифференциального уравнения в частных производных пятого порядка

Avıt ASANOV