## Differential Equations and Nonlinear Mechanics

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

#### 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.

#### Article information

Source
Differ. Equ. Nonlinear Mech., Volume 2007 (2007), Article ID 048527, 16 pages.

Dates
Revised: 24 January 2007
Accepted: 14 March 2007
First available in Project Euclid: 26 January 2017

https://projecteuclid.org/euclid.ijde/1485399781

Digital Object Identifier
doi:10.1155/2007/48527

Mathematical Reviews number (MathSciNet)
MR2318208

Zentralblatt MATH identifier
1156.70003

#### Citation

Saleh, M. M.; El-Kalla, I. L.; Ehab, M. M. Stochastic Finite Element Technique for Stochastic One-Dimension Time-Dependent Differential Equations with Random Coefficients. Differ. Equ. Nonlinear Mech. 2007 (2007), Article ID 048527, 16 pages. doi:10.1155/2007/48527. https://projecteuclid.org/euclid.ijde/1485399781

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