Recent work in the development of stochastic methods for multiple integrals over unbounded regions is reviewed and generalized. This includes randomization or deterministic rules, and new stochastic rules for integrals with multivariate Normal weight. Stochastic spherical–radial rules are also...

We give a simple presentation of an algorithm of selecting asymptotical first approximations of equations (algebraic and ordinary differential and partial differential). Here the first approximation of a solution of the initial equation is a solution of the corresponding first approximation of...

This paper deals with the aim of coupling multigrid generation of boundary-fitted grids with an effective domain decomposition technique. We present multiblock grid generation algorithms for efficient solutions of domain discretization problems. We propose the generation of structured grids by...

Dynamic reliability aims at estimating failure risks associated with very rare scenarios, while accounting for the system dynamic evolution. In a Monte Carlo game devised for this purpose, the most time consuming operation consists in performing these dynamic calculations, which are repeated in...

An efficient algorithm for the evaluation of the parametric sensitivities for mixed systems of differential and algebraic equations (DAEs) on computers involving multiple processors operating in parallel is presented. The algorithm derives its efficiency by decoupling the integration of the...

We deduce the spherical mean value relation for the pseudo-vibration elastic equation. We represent the kernel of the integral operator (averaging operator) in a special form having a probabilistic interpretation. This enables us to construct a random estimator for the solution which ensures an...

Digital system design and verification becomes more critical as systems grow in size and complexity. Also, simulation of digital systems become more costly in time and resources as systems get larger. This paper presents an effective simulation methodology for design error simulation using error...

The methodologies employed in the probabilistic safety assessment (PSA) of hazardous engineering systems have reached a high level of maturity. However, a few issues are still worth of further investigation in order to increase the confidence in the results obtained. In this view, in the past...

We discuss some non-standard applications of computer algebra in field theories based on the formal theory of differential equations and present a general programming environment for differential equations currently under construction in MuPAD.

This paper concerns a novel vibration exciter for rock drills. In conventional hammer drills vibrations are generated mechanically. The disadvantage of those systems is that the frequency of the vibrations is either constant or correlated to the rotational speed of the drill. This contribution...