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3 results on '"random linear diffusion models"'

1. Analytical-Numerical Solution of a Parabolic Diffusion Equation Under Uncertainty Conditions Using DTM with Monte Carlo Simulations

Author

Gilberto González Parra, Abraham J Arenas, and Miladys Cogollo

Subjects
random linear diffusion models, uncertainty conditions, fi- nite difference schemes, differential transformation method, analyticalnumerical solution., Technology, Science, Science (General), Q1-390
Abstract

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, 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. MSC: 35K10, 65C05, 65M99, 35R60

Published
2015
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2. Analytical-Numerical Solution of a Parabolic Diffusion Equation Under Uncertainty Conditions Using DTM with Monte Carlo Simulations.

Author

González-Parra, Gilberto, Arenas, Abraham J., and Cogollo, Miladys

Subjects
*DIFFUSION, *MONTE Carlo method, *FINITE element method, *DIFFERENCES, *DIFFUSION coefficients
Abstract

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. [ABSTRACT FROM AUTHOR]

Published
2015
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3. Solución numérico-analítica de una ecuación de difusión bajo condiciones de incertidumbre utilizando DTM y Monte Carlo

Author

Gilberto González Parra, Miladys R. Cogollo, Abraham J. Arenas, Grupo de Matemática Multidisciplinar (GMM), Fac. de Ingeniería, Universidad de los Andes, and Universidad de Córdoba, Facultad de Ciencias Básicas,Departamento de Matemáticas y Estadística

Subjects
differential transformation method, Diffusion equation, Monte Carlo method, analyticalnumerical solution, ECUACIONES DIFERENCIALES PARABÓLICAS - SOLUCIONES NUMÉRICAS, lcsh:Technology, Differential equations, parabolic --Numerical Solutions, DIFERENCIAS FINITAS, random linear diffusion models, Photon transport in biological tissue, fi- nite difference schemes, Applied mathematics, lcsh:Science, lcsh:Science (General), uncertainty conditions, Mathematics, INCERTIDUMBRE, lcsh:T, Numerical analysis, Uncertainty, Finite difference, ANÁLISIS NUMÉRICO, Finite volume method for one-dimensional steady state diffusion, Monte carlo method, MÉTODO DE MONTECARLO, Dynamic Monte Carlo method, Finite Differences, lcsh:Q, Algorithm, Random variable, lcsh:Q1-390
Abstract

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, 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, Un método numérico para resolver una ecuación parabólica general aleatoria lineal donde el coeficiente de difusión, el término fuente, las condiciones de contorno e iniciales incluyen la incertidumbre, se ha desarrollado -- Ecuaciones de difusión surgen en muchos campos de la ciencia y la ingeniería, y en muchos casos, existen la incertidumbres debido a los datos que no se pueden saber, o debido a errores en las mediciones y la variabilidad intrínseca -- Para modelar estas incertidumbres los parámetros correspondientes, coeficiente de difusión, término fuente, condiciones de contorno e iniciales, se suponen que son variables aleatorias con determinadas distribuciones de probabilidad -- Basándose en los resultados numéricos, se obtienen los intervalos de confianza y valores medios esperados para la solución -- Además, se obtienen con las soluciones numéricas-analíticas del método híbrido propuesto

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