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| Format: | Artículo científico |
| Language: | en |
| Published: |
Universidad EAFIT
2015
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| Online Access: | https://www.redalyc.org/articulo.oa?id=83540427003 |
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Table of Contents:
- Analytical-Numerical Solution of a Parabolic Diffusion Equation Under Uncertainty Conditions Using DTM with Monte Carlo Simulations Gilberto González-Parra Abraham J. Arenas Miladys Cogollo Ingeniería uncertainty conditions finite difference schemes analyticalnumerical solution Random linear diffusion models differential transformation method A numerical method to solve a general random linear parabolic equation where the diffusion coefficient, source term, boundary and initial conditions include uncertainty, is developed. Diffusion equations arise in many fields of science and engineering, and, in many cases, there are uncertainties due to data that cannot be known, or due to errors in measurements and intrinsic variability. In order to model these uncertainties the corresponding parameters, diffusion coefficient, source term, boundary and initial conditions, are assumed to be random variables with certain probability distributions functions. The proposed method includes finite difference schemes on the space variable and the differential transformation method for the time. In addition, the Monte Carlo method is used to deal with the random variables. The accuracy of the hybrid method is investigated numerically using the closed form solution of the deterministic associated equation. Based on the numerical results, confidence intervals and expected mean values for the solution are obtained. Furthermore, with the proposed hybrid method numerical-analytical solutions are obtained. 2015 artículo científico 1794-9165 https://www.redalyc.org/articulo.oa?id=83540427003 en http://www.redalyc.org/revista.oa?id=835 Ingeniería y Ciencia application/pdf Universidad EAFIT Ingeniería y Ciencia (Colombia) Num.22 Vol.11