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**Stochastic finite element technique for stochastic one-dimensional time-dependent differential equations with random coefficients.**
*(English)*
Zbl 1156.70003

Summary: We employ the stochastic finite element method (SFEM) for solving stochastic one-dimensional time-dependent differential equations with random coefficients. SFEM is used to have a fixed form of linear algebraic equations for polynomial chaos coefficients. 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 to the exact deterministic solution is studied numerically.

### MSC:

70-08 | Computational methods for problems pertaining to mechanics of particles and systems |

70L05 | Random vibrations in mechanics of particles and systems |

74J99 | Waves in solid mechanics |

74S05 | Finite element methods applied to problems in solid mechanics |

80A20 | Heat and mass transfer, heat flow (MSC2010) |

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\textit{M. M. Saleh} et al., Differ. Equ. Nonlinear Mech. 2007, Article ID 48527, 16 p. (2007; Zbl 1156.70003)

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