Dealing with Dependent Uncertainty in Modelling : A Comparative Study Case through the Airy Equation
Joint Authors
Villanueva Micó, Rafael Jacinto
Cortés López, Juan Carlos
Romero, J.-V.
Roselló, M.-D.
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-10-28
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Cortés López, Juan Carlos& Romero, J.-V.& Roselló, M.-D.& Villanueva Micó, Rafael Jacinto. 2013. Dealing with Dependent Uncertainty in Modelling : A Comparative Study Case through the Airy Equation. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-12.
https://search.emarefa.net/detail/BIM-459852
Modern Language Association (MLA)
Cortés López, Juan Carlos…[et al.]. Dealing with Dependent Uncertainty in Modelling : A Comparative Study Case through the Airy Equation. Abstract and Applied Analysis No. 2013 (2013), pp.1-12.
https://search.emarefa.net/detail/BIM-459852
American Medical Association (AMA)
Cortés López, Juan Carlos& Romero, J.-V.& Roselló, M.-D.& Villanueva Micó, Rafael Jacinto. Dealing with Dependent Uncertainty in Modelling : A Comparative Study Case through the Airy Equation. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-12.
https://search.emarefa.net/detail/BIM-459852
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-459852