Numerical Analysis, № 10, 2001

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.

We consider the three-dimensional Dirichlet problem for the equation Δu + (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...

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...

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...

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...

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.

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...

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...