Numerical modeling of boundary value problems for differential equations with random coefficients
2021 ◽
Vol 2099
(1)
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pp. 012065
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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.
2020 ◽
Vol 99
(3)
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pp. 75-85
1961 ◽
Vol 262
(1309)
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pp. 219-236
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1988 ◽
Vol 8
(3)
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pp. 239-248
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2020 ◽
Vol 16
(1)
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pp. 66-85
2011 ◽
Vol 57
(Supliment)
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1989 ◽
Vol 41
(10)
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pp. 1117-1129
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