Approximation of integral and differential operators and applications

Approximation of integral and differential operators and the corresponding applications are the subject of research. Since it belongs to the following areas: approximation theory, numerical analysis and functional analysis, we expect new results in these areas of mathematics, software implementation, as well as significant applications in telecommunications, computer sciences, physics and economics. Research will be focused to approximation of various classes of integral and differential operators, construction and analysis of interpolation and quadrature processes and solving integral equations and ordinary and partial differential equations. Besides linear operators, the problems with nonlinear operators will be treated in order to solve nonlinear problems. Special attention is paid to the methods for solving boundary and initial-boundary problems for partial differential equations. Constructive problems and stability and convergence of difference schemes will be investigated. A recent progress in the weighted polynomial approximation will be used to obtain efficient and stable methods for solving certain classes of integral equations and contour problems with differential equations. Approximation and development of stable algorithms for unbounded operators will be based on a regularization process. Integral representations of special functions will enable constructions of fast and efficient algorithms for calculating special functions and integral transformations.