Stochastic Finite Element Technique for Stochastic One-Dimension Time-Dependent Differential Equations with Random Coefficients

Saleh, M. M.; El-Kalla, I. L.; Ehab, M. M.

doi:https://doi.org/10.1155/2007/48527

International Journal of Differential Equations

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Research Article | Open Access

Volume 2007 | Article ID 048527 | https://doi.org/10.1155/2007/48527

Stochastic Finite Element Technique for Stochastic One-Dimension Time-Dependent Differential Equations with Random Coefficients

M. M. Saleh,¹I. L. El-Kalla,¹and M. M. Ehab¹

Academic Editor: Giuseppe Saccomandi

Received19 Sept 2006

Revised24 Jan 2007

Accepted14 Mar 2007

Published20 May 2007

Abstract

The stochastic finite element method (SFEM) is employed for solving stochastic one-dimension time-dependent differential equations with random coefficients. SFEM is used to have a fixed form of linear algebraic equations for polynomial chaos coefficients of the solution process. Four fixed forms are obtained in the cases of stochastic heat equation with stochastic heat capacity or heat conductivity coefficients and stochastic wave equation with stochastic mass density or elastic modulus coefficients. The relation between the exact deterministic solution and the mean of solution process is numerically studied.

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Copyright

Copyright © 2007 M. M. Saleh 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.

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