Dealing with dependent uncertainty in modelling: a comparative study case through the Airy equation
type: Item
instance of: scholarly article
title: Dealing with dependent uncertainty in modelling: a comparative study case through the Airy equation
zbMATH Open document ID: 1291.65018
DOI: 10.1155/2013/279642
published in: Abstract and Applied Analysis
publication date: 2014-06-23T00:00:00Z
review text: Summary: The consideration of uncertainty in differential equations leads to the emergent area of random differential equations. Under this approach, inputs become random variables and/or stochastic processes. Often one assumes that inputs are independent, a hypothesis that simplifies the mathematical treatment although it could not be met in applications. In this paper, we analyse, through the Airy equation, the influence of statistical dependence of inputs on the output, computing its expectation and standard deviation by Fröbenius and Polynomial Chaos methods. The results are compared with Monte Carlo sampling. The analysis is conducted by the Airy equation since, as in the deterministic scenario its solutions are highly oscillatory, it is expected that differences will be better highlighted. To illustrate our study, and motivated by the ubiquity of Gaussian random variables in numerous practical problems, we assume that inputs follow a multivariate Gaussian distribution throughout the paper. The application of Fröbenius method to solve Airy equation is based on an extension of the method to the case where inputs are dependent. The numerical results show that the existence of statistical dependence among the inputs and its magnitude entails changes on the variability of the output.
Mathematics Subject Classification ID: 65C30
Mathematics Subject Classification ID: 60H25
Mathematics Subject Classification ID: 34F05
zbMATH DE Number: 6306596
Wikidata QID: Q58915788
author: Juan Cortés
author: J.-V. Romero
author: M.-D. Roselló
author: R.-J. Villanueva
describes a project that uses: Mathematica
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/279642
OpenAlex ID: W2169704132
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description: scientific article; zbMATH DE number 6306596