## A-m.s.-stable numerical methods for solving stochastic differential equations in the Ito-sense

In this paper we investigate the asymptotic mean-square stability (m.s.-stability) of the family of numerical methods for solving SDE's in the Ito-sense generalizing Rosenbrock's type methods. The connection between the asymptotic m.s.-stability of the numerical method for solving SDE and the absolute stability of the corresponding Rosenbrock's type method are...

## Numerical analysis of stochastic auto-oscillating systems

The paper considers the questions of the numerical analysis of stochastic auto-oscillating systems. The low computer costs variable stepsize algorithms was constructed for solving the non-linear stochastic differential equations. There are given results of numerical experiments obtained with the help of the dialogue system "Dynamics and Control".

## Operator alternating-triangular method for the three-dimentional static problem in elasticity theory

To solve the tree-dimensional static problems in elasticity theory in the displacements a new class of effective iteration methods – factorized operator-triangular methods was studied. The additive expansion of the diagonal operator leads to the analogous expansion of the initial matrix operator in the sum of triangular-matrix operators. The degree...

## Locally two-sided approximate solutions in parabolic problems

By means of the fictitous regions method locally two-sided estimations the initial boundary value problem with the second order parabolic equation of the first type are obtained.

## On the explicit-implicit domain decomposition method without overlapping 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...

## Test nonlinear heat transfer equations with known solutions

A class of nonlinear 1-D parabolic equations with known solutions are introduced. The computer programs for estimation of the absolute errors of numerical methods are decribed.

## Convergence of variational splines I

Strong convergence of interpolating splines on the *imbedded meshes* is established without the assumption that the system of operators corresponding to the added interpolation conditions is *correct*. It is also shown that correctness of the system of operators is equivalent to the zero intersection of their kernels.

The necessary...

## Letter to Editorial Board

Letter to Editorial Board on the book of A.Yu. Bezhaev and V.A. Vasilenko **"Variational spline theory"**.