Volume 26, Issue 3

The inverse problem of heat flows and the corresponding problem of assimilation of ocean temperature data obtained from the international Argo Buoys system is formulated and studied. A solution algorithm is developed for this problem. Results of numerical experiments are presented.

A model of a many-dimensional homogeneous isotropic random field with an exponential correlation function and a given arbitrary one-dimensional distribution suitable for numerical implementation is constructed. The model is based on partition of the phase space by a field of random hyperplanes determined by some parametric Poisson point field. The possibility of application of this model to the solution of stochastic problems of radiation balance based on the combination of the methods of ‘double randomization’ and ‘maximal section’ is discussed.

The problem of numerical estimation of the functionals of the solutions to a Boltzmann type nonlinear equation in the kinetic model of a vehicle traffic flow with separated acceleration is considered. The authors construct a second-kind integral equation for the original probabilistic model of a vehicle traffic flow, which is related to a linear N -particle model of the vehicle system evolution. Weighted Monte Carlo methods are proposed for the estimation of the functionals of the solution to the obtained equation. The practical suitability of this approach to the solution of traffic problems is demonstrated by numerical experiments. It should be noted that, in contrast to the previous papers, the authors do not use an artificial time step not included in the original traffic flow model.

Linear systems of ordinary differential and algebraic equations modelling passive integral circuits consisting of resistors and capacitors (RC-circuits) are considered. A method for the fast calculation of signal delay is such circuits is proposed. For this purpose, the input signal is approximated by several first Laguerre functions and the output of the system is obtained in the form of a sum of several Laguerre functions and one of the eigenvalues of the matrix pencil corresponding to the system (spectral correction of the solution). For the case of approximation of the input and output signals by two Laguerre functions, criteria are proposed for a priori determination whether sufficiently good approximation is guaranteed for the particular system. Results of numerical experiments with industrial design tests are presented and discussed.

In this paper QTT-approximations to elliptic solution operators with constant coefficients in d -dimensional cube are constructed. The ε -accurate representations of the Frobenius norm can be computed with the complexity O ( d log q ε –1 ), where d ⩾ 2 is the spatial dimension, and q ⩾ 2 is some fixed constant.

The theory of scalar and vector probabilistic–algebraic algorithms of the Monte Carlo method used in the solution of systems of integral equations is detailed and refined in the paper. A dual representation of the mean square of a vector estimate is constructed. Scalar algorithms are formulated, and a comparison of vector and scalar estimates of the solution is given for the first time. A criterion of finiteness of vector estimate variance is constructed on this basis.