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Journal of Applied MathematicsVolume 2014 2014, Article ID 843714, 9 pages

Research Article

Electrical and Computer Engineering Department, Engineering Faculty, Effat University, Jeddah 21478, Saudi Arabia

Engineering Mathematics and Physics Department, Engineering Faculty, Cairo University, Giza 12221, Egypt

Mathematics Department, Science College, University of Dammam, Dammam 31451, Saudi Arabia

Received 5 April 2014; Accepted 8 June 2014; Published 24 June 2014

Academic Editor: Song Cen

Copyright © 2014 Mohamed A. El-Beltagy and Noha A. Al-Mulla. 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.


In the current work, the Wiener-Hermite expansion WHE is used to solve the stochastic heat equation with nonlinear losses. WHE is used to deduce the equivalent deterministic system up to third order accuracy. The solution of the equivalent deterministic system is obtained using different techniques numerically and analytically. The finite-volume method FVM with Pickard iteration is used to solve the equivalent system iteratively. The WHE with perturbation technique WHEP is applied to deduce more simple and decoupled equivalent deterministic system that can be solved numerically without iterations. The system resulting from WHEP technique is solved also analytically using the eigenfunction expansion technique. The Monte-Carlo simulations MCS are performed to get the statistical properties of the stochastic solution and to verify other solution techniques. The results show that higher-order solutions are essential especially in case of nonlinearities where non-Gaussian effects cannot be neglected. The comparisons show the efficiency of the numerical WHE and WHEP techniques in solving stochastic nonlinear PDEs compared with the analytical solution and MCS.

Autor: Mohamed A. El-Beltagy and Noha A. Al-Mulla



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