About this Journal Submit a Manuscript Table of Contents
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.

Linked References

  1. M. Necati Özişik, Boundary Value Problems of Heat Conduction, Dover, New York, NY, USA, 1968.
  2. R. Chiba, “Stochastic heat conduction analysis of a functionally grade annular disc with spatially random heat transfer coefficients,” Applied Mathematical Modelling, vol. 33, no. 1, pp. 507–523, 2009. View at Publisher · View at Google Scholar
  3. Y. Li and S. Long, “A finite element model based on statistical two-scale analysis for equivalent heat transfer parameters of composite material with random grains,” Applied Mathematical Modelling, vol. 33, no. 7, pp. 3157–3165, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  4. J. C. Cortés, L. Jódar, L. Villafuerte, and R. J. Villanueva, “Computing mean square approximations of random diffusion models with source term,” Mathematics and Computers in Simulation, vol. 76, no. 1–3, pp. 44–48, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  5. L. Jódar, J. C. Cortés, and L. Villafuerte, “A discrete eigenfunctions method for numerical solution of random diffusion models,” in Proceedings of the Conference on Differential and Difference Equations and Applications, pp. 457–466, 2005.
  6. J.-C. Cortés, L. Jódar, M.-D. Roselló, and L. Villafuerte, “Solving initial and two-point boundary value linear random differential equations: a mean square approach,” Applied Mathematics and Computation, vol. 219, no. 4, pp. 2204–2211, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  7. A. G. Madera, “Modelling of stochastic heat transfer in a solid,” Applied Mathematical Modelling, vol. 17, no. 12, pp. 664–668, 1993. View at Publisher · View at Google Scholar
  8. A. G. Madera and A. N. Sotnikov, “Method for analyzing stochastic heat transfer in a fluid flow,” Applied Mathematical Modelling, vol. 20, no. 8, pp. 588–592, 1996. View at Publisher · View at Google Scholar
  9. T. T. Soong, Random Differential Equations in Science and Engineering, Academic Press, New York, NY, USA, 1973. View at MathSciNet
  10. L. Villafuerte, C. A. Braumann, J.-C. Cortés, and L. Jódar, “Random differential operational calculus: theory and applications,” Computers & Mathematics with Applications, vol. 59, no. 1, pp. 115–125, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  11. L. Arnold, Stochastic Differential Equations: Theory and Applications, John Wiley & Sons, New York, NY, USA, 1974. View at MathSciNet
  12. E. C. Titchmarsch, The Theory of Functions, Oxford University Press, New York, NY, USA, 2nd edition, 1939.
  13. G. Calbo, J.-C. Cortés, and L. Jódar, “Random Hermite differential equations: mean square power series solutions and statistical properties,” Applied Mathematics and Computation, vol. 218, no. 7, pp. 3654–3666, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  14. M. Loève, Probability Theory I and II, vol. 45 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 4th edition, 1977. View at MathSciNet
  15. J. C. Cortés, P. Sevilla-Peris, and L. Jódar, “Analytic-numerical approximating processes of diffusion equation with data uncertainty,” Computers & Mathematics with Applications, vol. 49, no. 7-8, pp. 1255–1266, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  16. A. J. Jerri, Integral and Discrete Transforms with Applications and Error Analysis, vol. 162 of Pure and Applied Mathematics, Marcel Dekkers, New York, NY, USA, 1992. View at MathSciNet
  17. J. Dieudonné, Foundations of Modern Analysis, Academic Press, New York, NY, USA, 1969. View at MathSciNet