# Sinaiskii E. S.

### Approximation method in problems of potential theory

Ukr. Mat. Zh. - 2000. - 52, № 6. - pp. 773–782

We investigate the properties of the Dzyadyk approximation method in the case of a binomial function. We study conditions under which an estimate for the relative error of approximation in the uniform metric is exact. The results obtained are applied to certain problems in potential theory.

### On one stochastic model that leads to a stable distribution

Ukr. Mat. Zh. - 1997. - 49, № 11. - pp. 1572–1579

We consider an integral equation describing the contagion phenomenon, in particular, the equation of the state of a hereditarily elastic body, and interpret this equation as a stochastic model in which the Rabotnov exponent of fractional order plays the role of density of probability of random delay time. We invesgigate the approximation of the distribution for sums of values with a given density to the stable distribution law and establish the principal characteristics of the corresponding renewal process.

### Approximation method for the problems of mechanics of inhomogeneous hereditarily elastic bodies

Ukr. Mat. Zh. - 1994. - 46, № 9. - pp. 1234–1245

We consider a boundary-value problem of mechanics of inhomogeneous hereditarily elastic bodies formulated as a linear equation with an operator of fractional integration, partial derivatives with respect to time and spatial variables, and polynomial-type coefficients of one of the variables. An approximate solution of this problem is constructed according to Dzyadyk's a-method combined with the use of the Laplace transformation. It is proved that the errors of the approximation of the required function and its derivatives decrease in geometric progression.

### An approximation method in a boundary value problem with partial derivatives

Ukr. Mat. Zh. - 1990. - 42, № 6. - pp. 812–816

### An approximation method in a boundary-value problem for a linear differential equation with polynomial coefficients

Ukr. Mat. Zh. - 1988. - 40, № 2. - pp. 248-253

### Asymptotic behavior of the solution of the Dirichlet problem for a differential operator with a small parameter

Ukr. Mat. Zh. - 1984. - 36, № 6. - pp. 738 – 737