Solution of the Stochastic Heat Equation with Nonlinear Losses Using Wiener-Hermite Expansion
Joint Authors
al-Mulla, Noha A.
El-Beltagy, Mohamed A.
Source
Journal of Applied Mathematics
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-06-24
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
El-Beltagy, Mohamed A.& al-Mulla, Noha A.. 2014. Solution of the Stochastic Heat Equation with Nonlinear Losses Using Wiener-Hermite Expansion. Journal of Applied Mathematics،Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-502738
Modern Language Association (MLA)
El-Beltagy, Mohamed A.& al-Mulla, Noha A.. Solution of the Stochastic Heat Equation with Nonlinear Losses Using Wiener-Hermite Expansion. Journal of Applied Mathematics No. 2014 (2014), pp.1-9.
https://search.emarefa.net/detail/BIM-502738
American Medical Association (AMA)
El-Beltagy, Mohamed A.& al-Mulla, Noha A.. Solution of the Stochastic Heat Equation with Nonlinear Losses Using Wiener-Hermite Expansion. Journal of Applied Mathematics. 2014. Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-502738
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-502738