# Monte Carlo method

## Quantifying uncertainty of a mathematical model of drug transport in tumors

This paper presents a numerical simulation in the two-dimensional for a system of PDE governing drug transport in tumors with random coefficients, which is described  as a random field.  The continuous stochastic field is approximated by a finite number of random variables via the Karhunen–Loève expansion and transform the stochastic problem into a determinate one with a parameter in high dimension.  Then we apply a finite difference scheme and the Euler–Maruyama Integrator in time.  The Monte Carlo method is used to compute corresponding simple averages.  We compute the error estimate usin

## Method of statistical imitation, its creator S. Ulam and basic principles of application for random processes modeling

The article is dedicated to famous Lviv residents, the author of the Monte Carlo method, and mathematician Marco Katsu. The method of Monte Carlo methodical algorithms for modeling statistical regularities of light passage through optically inhomogeneous media is briefly described in the article

## THEORETICAL ANALYSIS OF EXISTING CONCEPTS TO EVALUATE THE NON-FAILURE OF RC STRUCTURES IN OPERATION

The article presents a theoretical analysis of existing concepts to evaluate the non-failure of RC structures in operation. To perform the analysis, the authors considered a number of scientific works of both Ukrainian and foreign researchers. The main focus was on works in which the model of the stochastic nature of the RC structure operation included random parameters of acting loads, as well as the reserve of its bearing capacity and serviceability (geometric dimensions of cross sections of constructive members, strength and deformation characteristics of materials, etc.).

## VIRTUAL MEASURING INSTRUMENTS AS MEANS OF UNCERTAINTY EVALUATION

Modern measuring instruments as highly technological, precise, multi-functional tools today are complex systems, and estimation of their uncertainty turns into a non-trivial task of science. To provide information about the probability of results, their convergence, and reproducibility, it is necessary to analyze the task-oriented measurement uncertainty. As an approach to determining the uncertainty of complex systems, to avoid the need for professionally experienced personnel and expensive "artifacts" used for evaluation, there is a method of a so-called virtual measuring instrument.

## THE EFFECT OF RANDOM DEVIATIONS ON UNCERTAINTY OF EXTREME OBSERVATIONS

An attention is considered to analysis of instrumental component of result’s uncertainty. While production control in industry, the mentioned component for concrete measuring instrument with the concrete measurement results has to be determined and analyzed. Important is the question of random impacts effect on to uncertainty of extreme (minimum or maximum) observations.