## Certain aspects of application of numerical methods for solving SDE systems

The problems of determining the structure of numerical method, the choice of its parameters, analysis of meansquare or weak convergence of the numerical solution to the true one are much more complicated for systems of SDE, than for those of ODE. Nevertheless, many theoretical and practical ideas of the numerical...

## Modified Runge-Kutta method

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 constracting fundamental equations of RK-method...

## On the domain decomposition method for parabolic problems

The paper deals with studying the domain decomposition algorithm with overlapping subdomains. This algorithm is based on the splitting method and uses the additive presentation of some bilinear form. Earlier this method was described for two subdomains. In our consideration we formulate the decomposition algorithm for an arbitrary number of...

## Variational rational splines of many variables

The purpose of this paper is to construct the interpolating function as a ratio of two splines. The numerator and the denominator of this ratio minimize some combined variational functional on the set of pairs of functions which satisfy interpolating conditions and some additional restrictions. Such a construction was proposed...

## Convergence of quintic spline interpolants in terms of a local mesh ratio

In this paper we give an algorithm for finding the bounds for a ratio of two neighbouring mesh steps which provide the convergence of odd-degree spline interpolants and their derivatives. For the quintic splines numerical values are obtained which improve the estimates by S. Friedland, C. Micchelli.

## Quasi-polynomial finite elements in elliptic boundary value problems with small parameter

The uniform error estimates with respect to a small parameter are obtained here for the finite element approximation of the elliptic boundary value problem with a small parameter. The space of trial functions is the space of special *L*-splines with the basis of local functions.