## Multivariate approximation at huge scattered meshes

The paper deals with the "true" multi-dimensional interpolation problem at scattered meshes with a huge number of interpolating points. For its solution we suggest here a new numerical technology consisting in partitioning of the problem on a number of subproblems and in a successive glueing of solutions to the subproblems...

## On approximations of the charge transfer equation in semiconductor

In this paper the approximations of diffusion-convection equation, describing the charge transfer in semiconductors are concidered.

## On energy estimates for preconditioning grid parabolic problems

The paper deals with studying of some preconditioning operators providing unconditional convergence of difference schemes for solving parabolic problems. Three examples of such operators are considered. There are a preconditioner of the domain decomposition method of the Neumann-Dirichlet type and two preconditioners of the fictitious domain methods for the Neumann...

## On one modification of Marchuk-Kuzin's scheme for parabolic equations with mixed derivatives

In the article, we propose and study one modification of the finite element splitting algorithm for the solution to the Neumann boundary parabolic problem with mixed derivatives. We consider the simplest equations with constant coefficients without advective terms. In our case, for the Neumann problem, the error estimate contains the...

## On the theory of algebraic multilevel incomplete factorization methods for the Stieltjes matrices

Recently an algebraic multilevel incomplete factorization method for solving large linear systems with the Stieltjes matrices has been proposed. This method is a combination of two well-known techniques: algebraic multilevel (AMLI) and incomplete factorization. However, the efficiency of this method strongly depends on the choice of the relaxation parameter *θ...*

## The program of Delaunay triangulatoin construction for the domain with the piecewise smooth boundary

In this paper we describe the program of triangular mesh construction with Delaunay properties for the domains, which boundaries consist of straight lines and arcs of circles and ellipses. There was used the geometric preprocessor TTNS in order to form the discret similarity for the calculated domain and to construct...

## Numerical solution to Volterra integral equations of the first kind by implicit Runge-Kutta method of high accuracy

The analog of the implicit Runge-Kutta method applied to Volterra integral equations of the first kind is considered. It allows to obtain the results of high accuracy under a sufficient simplicity and stability of used algorithm. The estimation of numerical results for a fixed time step is performed. A special...