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2014 Solution of the Stochastic Heat Equation with Nonlinear Losses Using Wiener-Hermite Expansion
Mohamed A. El-Beltagy, Noha A. Al-Mulla
J. Appl. Math. 2014: 1-9 (2014). DOI: 10.1155/2014/843714


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.


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Mohamed A. El-Beltagy. Noha A. Al-Mulla. "Solution of the Stochastic Heat Equation with Nonlinear Losses Using Wiener-Hermite Expansion." J. Appl. Math. 2014 1 - 9, 2014.


Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07131915
MathSciNet: MR3228143
Digital Object Identifier: 10.1155/2014/843714

Rights: Copyright © 2014 Hindawi


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