integral equation

Finite element approximations in projection methods for solution of some Fredholm integral equation of the first kind

Approximation properties of B-splines and Lagrangian finite elements in Hilbert spaces of functions defined on surfaces in three-dimensional space are investigated.  The conditions for the convergence of Galerkin and collocation methods for solution of the Fredholm integral equation of the first kind for the simple layer potential that is equivalent to the Dirichlet problem for Laplace equation in $\mathbb{R}^3$ are established.  The estimation of the error of approximate solution of this problem, obtained by means of the potential theory methods, is determined.

Three-input integral model of the recovery problem of antenna signals with interference

The problem of increasing the resolution power of an antenna through input signal recovery using the computer implementation of a mathematical model in the form of the system of three Fredholm integral equations of the first kind is examined. To solve the system of linear integral equations, regularizating algorithms and corresponding softwares based on generalized Tikhonov and Lavrentiev methods with determination of a regularization parameter by means of the model experiments technique have been developed.