## Stability of numerical methods for solving stochastic differential equations

This paper deals with the problem of mean-square stability of numerical methods for solving SDE's. We introduce the notion of the stiff in a mean-square sense system of SDE's, the practical verification of which is not difficult. In the capacity of the investigated family of numerical methods the generalization of...

## Data compression with ΣΠ-approximations based on splines

The paper contains short description of ΣΠ-algorithm for the approximation of the function with two independent variables by the sum of products of one-dimensional functions. Some realizations of this algorithm based on the continuous and discrete splines are presented here. Few examples concerning with compression in the solving of approximation...

## On iterative solving of linear algebraic equations in p-h-version of finite element method

The goal of this paper is investigation of the efficiency of iterative preconditioned cojugate gradient methods for solving linear systems of equations which arise in *p*-*h*-version of finite element methods. The results of numerical experiments are presented for the model boundary value problem with different values of...

## Generation of dynamic Delaunay triangulations

Non-stationary problems of finite element solutions require an efficient generation of sequential meshes with minor changes in density functions of points distribution. The Delaunay meshes sequential generation is studied in terms of successive insertions and removings of points following changes in density function.

## Modified Runge-Kutta method. II

Modern Runge-Kutta method of solving ODE bears a slight resemblance with the classical (explicit) method and is based on the transformation of the differential equation to the integral one. The contents of the mathematical theory was formulated by J.C. Butcher et all. Nevertheless, the technique of constructing fundamental equations of RK-method...

## On uniform convergence of Scharfetter's scheme

The transfer of charge carries in a semiconductor device for stationary conditions is described by elliptic differential equations with oscilating coefficients. The uniform convergence of one-dimensional Scharfetter's scheme on the whole interval is shown in this paper.

## On the explict-implict domain decomposition method for parabolic problems

The paper deals with studying the domain decomposition algorithm on two subdomains, where for one of them, which contains sufficiently small number of nodes, is used explicit scheme with small time step, and for another subdomain may be used effective direct algorithm (for example, subdomain is parallelepiped). This method is...

## Short review on variational approach in abstract splines

The abstract variational theory of splines in the Hilbert space originated from the well-known paper by M. Atteia (1965) and supported by P.J. Laurent's researches (1968, 1973) is today a well-developed field in the approximation theory. We mean that the forthcoming researches in abstract theory were initiated by the problem of high-quality...