## Differential Equations and Nonlinear Mechanics

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

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

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

#### 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**

Received: 19 September 2006

Revised: 24 January 2007

Accepted: 14 March 2007

First available in Project Euclid: 26 January 2017

**Permanent link to this document**

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