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Abstract and Applied Analysis
Volume 2013, Article ID 983839, 10 pages
http://dx.doi.org/10.1155/2013/983839
Research Article

Solving Continuous Models with Dependent Uncertainty: A Computational Approach

1Instituto Universitario de Matemática Multidisciplinar, Building 8G, 2nd Floor Access C, Universitat Politècnica de València, 46022 Valencia, Spain
2Departamento de Estadística e Investigación Operativa, Facultad de Ciencias Matemáticas, Universitat de València, Avenida Doctor Moliner S/N, Burjassot, 46100 Valencia, Spain

Received 26 April 2013; Accepted 5 September 2013

Academic Editor: Ademir Fernando Pazoto

Copyright © 2013 J.-C. Cortés et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [7 citations]

The following is the list of published articles that have cited the current article.

  • Frederico Martins Alves da Silva, Augusta Finotti Brazão, and Paulo Batista Gonçalves, “Influence of Physical and Geometrical Uncertainties in the Parametric Instability Load of an Axially Excited Cylindrical Shell,” Mathematical Problems in Engineering, vol. 2015, pp. 1–18, 2015. View at Publisher · View at Google Scholar
  • J. Calatayud, J.-C. Cortés, and M. Jornet, “Uncertainty quantification for nonlinear difference equations with dependent random inputs via a stochastic Galerkin projection technique,” Communications in Nonlinear Science and Numerical Simulation, 2018. View at Publisher · View at Google Scholar
  • Julia Gregori, Juan López, and Marc Sanz, “Some Notes to Extend the Study on Random Non-Autonomous Second Order Linear Differential Equations Appearing in Mathematical Modeling,” Mathematical and Computational Applications, vol. 23, no. 4, pp. 76, 2018. View at Publisher · View at Google Scholar
  • Julia Calatayud, Juan Carlos Cortés, Marc Jornet, and Rafael Jacinto Villanueva, “Computational uncertainty quantification for random time-discrete epidemiological models using adaptive gPC,” Mathematical Methods in the Applied Sciences, 2018. View at Publisher · View at Google Scholar
  • Julia Calatayud, Juan Carlos Cortés, and Marc Jornet, “Computational uncertainty quantification for random non-autonomous second order linear differential equations via adapted gPC: A comparative case study with random Fröbenius method and Monte Carlo simulation,” Open Mathematics, vol. 16, no. 1, pp. 1651–1666, 2018. View at Publisher · View at Google Scholar
  • J. Calatayud, J.‐C. Cortés, and M. Jornet, “ On the Legendre differential equation with uncertainties at the regular‐singular point 1: L p ( Ω ) random power series solution and approximation of its statistical moments ,” Computational and Mathematical Methods, vol. 1, no. 4, 2019. View at Publisher · View at Google Scholar
  • J. Calatayud, J.-C. Cortés, and M. Jornet, “Improving the Approximation of the First- and Second-Order Statistics of the Response Stochastic Process to the Random Legendre Differential Equation,” Mediterranean Journal of Mathematics, vol. 16, no. 3, 2019. View at Publisher · View at Google Scholar