Differential Equations and Nonlinear Mechanics
Volume 2007 (2007), Article ID 48527, 16 pages
doi:10.1155/2007/48527

Stochastic finite element technique for stochastic one-dimensional 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.