## Two level iterative type explicit schemes

In the paper, we continue the investigation carried out earlier, namely, another approach to design two level explicit schemes for solution of the boundary value parabolic problems is proposed.

## The Monte Carlo method for conjugate stationary diffusion equation with special item

We consider the three-dimensional Dirichlet problem for the equation
Δ*u* + (*v*, grad *u*) + *cu* = -*g*, *u*|Γ = *ψ*
in a domain Ω with the boundary Γ, which is assumed simply connected and piecewise smooth. We suppose the functions *v*, *c*, and...

## Bias of the Bird type estimator

We consider a system of spatially homogeneous Smoluchowski equations. We will suggest that the coagulation coefficients are finite. Among numerical methods for solving this problem, Monte Carlo algorithms, based on the direct simulation of the coagulation process in a model particle system, play an important role. Note, that the Smoluchowski...

## Monte Carlo methods for estimating the time dependence during the process of radiation transfer

We consider the problem of estimating the reflected light intensity. This problem arises when studying the interference of backward scattering in laser sensing of the ocean from the atmosphere. Let *tα* be the time it takes for the intensity to achieve some asymptotical function. In this paper, a new...

## Parametric estimate of the solution of the boundary value problem by the Monte Carlo method

One of advantages of the Monte Carlo methods consists in capability to evaluate various functionals by weighting estimates, for instance, it is possible to evaluate the eigenvalues by using the estimate of the parametric derivations of the solution. The other significant application of weight estimates consists in capability of parametric...

## A variant of the residual correction method for the numerical solution of the Laplace and the Poisson equations

The high accuracy numerical solution of the Laplace or the Poisson equation is reduced to a sequence of the more simple finite difference problems of the second order accuracy. Some algorithms to realize effectively this scheme are discussed.

## Numerical simulation of a special class of non-homogeneous Gaussian fields

We consider an algorithm for the stochastic simulation of the Gaussian three-dimensional fields with a discrete argument and with regard the dependence of horizontal correlation functions on the vertical coordinate. The area for uses for the algorithm in question for a specific class of correlation functions of the horizontal fields...

## Condition number of collocation method on a quasiuniform grid for the integral equation of the 1st kind with logarithmic singularity

The paper is devoted to the substantiation of the direct numerical method for the integral equation of the first kind with logarithmic singularity on the closed curve; it is based on the piecewise-linear approximation of unknown function from its values at quasiuniform grid and collocation condition in the same gridpoints...