[1] O. H. Galal, W. El-Tahan, M. A. El-Tawil and A. A. Mahmoud, “Spectral SFEM Analysis of Structures with Stochastic Parameters under Stochastic Excitation,” Structural Engineering and Mechanics, Vol. 28 No. 3, 2008, pp. 281-294.
[2] O. H. Galal, “The Solution of Stochastic Linear Partial Differential Equation Using SFEM through Neumann and Homogeneous Chaos Expansions,” Ph.D. Thesis, Cairo University, Cairo, 2005.
[3] S. Rahman and H. Xu, “A Meshless Method for Computational Structure Mechanics,” International Journal for Computational Methods in Engineering Science and Mechanics, Vol. 6, No. 1, 2005, pp. 41-58. doi:10.1080/15502280590888649
[4] M. Kaminski, “Stochastic Perturbation Approach to Engineering Structure Variability by the Finite Difference Method,” Journal of Sound and Vibration, Vol. 251 No. 4, 2002, pp. 651-670. doi:10.1006/jsvi.2001.3850
[5] G. Stefanou, “The Stochastic Finite Element Methods: Past, Present and Future,” Computer Methods in Applied Mechanics and Engineering, Vol. 198, No. 9-12, 2009, pp. 1031-1051. doi:10.1016/j.cma.2008.11.007
[6] M. Shinozuka and T. Nomoto, “Response Variability Due to Spatial Randomness of Material Properties,” Technical Report, Columbia University, New York, 1980.
[7] A. Henriques, J. Veiga, J. Matos and J. Delgado, “Uncertainty Analysis of Structural Systems by Perturbation Techniques,” Journal of Structural and Multidisciplinary Optimization, Vol. 35 No. 3, 2008, pp. 201-212. doi:10.1007/s00158-007-0218-z
[8] R. Ghanem and P. D. Spanos, “Stochastic Finite Elements: A Spectral Approach,” 2nd Edition, Dover, New-York, 2002.
[9] H. Panayirci, “Computational Strategies for Efficient Stochastic Finite Element Analysis of Engineering Structures,” Ph.D. Thesis, University of Innsbruck, Innsbruck, 2010.
[10] J. Hurtado, “Analysis of One Dimensional Stochastic Finite Element Using Neural Network,” Probabilistic Engineering Mechanics, Vol.17, No. 1, 2001, pp. 35-44.
[11] M. A. El-Beltagy, O. H. Galal and M. I. Wafa, “Uncertainty Quantification of a 1-D Beam Deflection Due to Stochastic Parameters,” International Conference on Numerical Analysis and Applied Mathematics, Halkidiki, 19-25 September 2011, pp. 2000-2003. doi:10.1063/1.3637007.
[12] J. D. Cole, “On a Quasilinear Parabolic Equations Occurring in Aerodynamics,” Quarterly of Applied Mathematics, Vol. 9, 1951, pp. 225-236.
[13] J. D. Logan, “An Introduction to Nonlinear Partial Differential Equations,” Wily-Interscience, New York, 1994.
[14] L. Debtnath, “Nonlinear Partial Differential Equations for Scientist and Engineers,” Birkhauser, Boston, 1997.
[15] G. Adomian, “The Diffusion-Brusselator Equation,” Computers & Mathematics with Applications, Vol. 29, No. 5, 1995, pp. 1-3. doi:10.1016/0898-1221(94)00244-F
[16] C. Fletcher, “Burgers’ Equation: A Model for All Reasons,” Numerical Solutions of Partial Differential Equations, North-Holland Pub. Co., Holland, 1982.
[17] A. B. Stephens, R. B. Kellogg and G. R. Shubin, “Uniqueness and the Cell Reynolds Number,” SIAM Journal on Numerical Analysis, Vol. 17, No. 6, 1980.
[18] O. Schenk and K. G?rtner, “Solving Unsymmetric Sparse Systems of Linear Equations with PARDISO,” Journal of Future Generation Computer Systems, Vol. 20, No. 3, 2004, pp. 475-487. doi:10.1016/j.future.2003.07.011
[19] O. Schenk and K. G?rtner, “On Fast Factorization Pivoting Methods for Symmetric Indefinite Systems,” Electronic Transactions on Numerical Analysis, Vol. 23, 2006, pp. 158-179.