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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 676372, 9 pages
http://dx.doi.org/10.1155/2013/676372
Research Article

Analytic-Numerical Solution of Random Boundary Value Heat Problems in a Semi-Infinite Bar

Instituto Universitario de Matemática Multidisciplinar, Building 8G Access C, 2nd Floor, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain

Received 9 July 2013; Accepted 27 August 2013

Academic Editor: Benito Chen-Charpentier

Copyright © 2013 M.-C. Casabán 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.

Abstract

This paper deals with the analytic-numerical solution of random heat problems for the temperature distribution in a semi-infinite bar with different boundary value conditions. We apply a random Fourier sine and cosine transform mean square approach. Random operational mean square calculus is developed for the introduced transforms. Using previous results about random ordinary differential equations, a closed form solution stochastic process is firstly obtained. Then, expectation and variance are computed. Illustrative numerical examples are included.