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Abstract and Applied Analysis
Volume 2016, Article ID 5391368, 7 pages
http://dx.doi.org/10.1155/2016/5391368
Research Article

Approximating the Solution Stochastic Process of the Random Cauchy One-Dimensional Heat Model

1Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera, s/n, 46022 València, Spain
2Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt

Received 9 August 2016; Accepted 27 September 2016

Academic Editor: Francisco J. S. Lozano

Copyright © 2016 A. Navarro-Quiles 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 numerical solution of the random Cauchy one-dimensional heat model. We propose a random finite difference numerical scheme to construct numerical approximations to the solution stochastic process. We establish sufficient conditions in order to guarantee the consistency and stability of the proposed random numerical scheme. The theoretical results are illustrated by means of an example where reliable approximations of the mean and standard deviation to the solution stochastic process are given.