Volume 21, Issue 3

This paper deals with the computation of the reducing subspace associated with the rightmost part of the spectrum of a large matrix pencil A –λ B with B = diag( I ,0). Two variants of the Jacobi-Davidson method are discussed and developed. One is based on the Euclidean inner product and the second on the semi-inner product induced by B . Both versions use real arithmetics and incorporate an efficient deflation procedure. Numerical results are reported.

We propose an efficient algorithm in the direct statistical simulation method for an approximate solution to the Cauchy problem for a nonlinear spatially inhomogeneous coagulation equation that describes the coagulation of particles together with their diffusion transfer. The use of the majorant frequency principle allows one to attain a linear dependence of the computational costs of the algorithm on the initial number of test particles. The main properties of the algorithm include a special markovian random process and a splitting scheme with respect to physical processes. We consider in detail the spatially one-dimensional case of the above equation. For this case, we develop a special procedure for transforming the ensemble of test particles and propose a method for the preliminary estimation of the parameters of the computational algorithm.

In this paper we consider numerical algorithms for stochastic simulation of time series and space fields, which take into account the specific character of real hydrometeorological processes and fields.We propose and investigate a special algorithm for simulating inhomogeneous threedimensional fields of a discrete argument in which the field correlation structure is height-dependent. We consider two special stochastic models of binary stationary time sequences related to precipitation series. We give model estimates for the distributions of arid and rainy periods, which are needed to investigate extreme precipitation regimes.

We formalize the concept of the 'age disease aggravation index' in humans. By mathematical modelling methods using experimental data we prove a stochastic dependence of the aggravation index of age diseases in a human on the life spans of his parents. A crucial difference in the character of this dependence for men and women is established.

In this paper we study an algorithm for estimating the solution of an integral second-kind equation by values at mesh nodes which are obtained using a local estimate of the Monte Carlo method. We consider a complete optimization problem in which, in addition to the number of mesh nodes and the number of trajectories selected in the Monte Carlo method, we select an optimum transition density specifying a corresponding Markov chain. This density is chosen from a class of piecewise constant approximations of optimal density in the dependent test method in the space L 2 (V).