Some Boundary Value Problems for Generalized Random Fields

1991 ◽  
Vol 35 (4) ◽  
pp. 707-724 ◽  
Author(s):  
Yu. A. Rozanov
Keyword(s):  
Boundary Value Problems ◽  
Random Fields ◽  
Boundary Value

Statistical Simulation of Accidental Loads in the Problems of Constructional Mechanics

2015 ◽  
Vol 1122 ◽  
pp. 249-252
Author(s):  
Bohdan Yeremenko ◽  
Anatolii Pashko ◽  
Svitlana Terenchuk
Keyword(s):  
Spectral Density ◽  
Boundary Value Problems ◽  
Random Fields ◽  
Boundary Value ◽  
Structural Mechanics ◽  
Statistical Simulation ◽  
Simulation Results

In this paper, we consider a method of simulation of random fields with known spectral density. The simulation results used to solve problems of structural mechanics, which describes the boundary value problems

scholarly journals Numerical modeling of boundary value problems for differential equations with random coefficients

2021 ◽  
Vol 2099 (1) ◽  
pp. 012065
Author(s):  
B S Dobronets ◽  
O A Popova ◽  
A M Merko
Keyword(s):  
Numerical Modeling ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Random Fields ◽  
Boundary Value ◽  
Probability Density Functions ◽  
Random Coefficients ◽  
Independent Random Variables ◽  
Density Functions ◽  
Elliptic Type

Abstract This paper deals with the numerical modeling of differential equations with coefficients in the form of random fields. Using the Karhunen-Lo´eve expansion, we approximate these coefficients as a sum of independent random variables and real functions. This allows us to use the computational probabilistic analysis. In particular, we apply the technique of probabilistic extensions to construct the probability density functions of the processes under study. As a result, we present a comparison of our approach with Monte Carlo method in terms of the number of operations and demonstrate the results of numerical experiments for boundary value problems for differential equations of the elliptic type.

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