### Abstract

A numerical solution to an initial boundary value problem governing the probability of failure of a randomly accelerated free particle is obtained using a Petrov-Galerkin finite element method. This direct solution is the first successful one, and no others have been reported in the literature. A solution of the Pontriagin-Vitt equation for the time to first passage of the particle is obtained first: in this case an analytical solution is available and used to evaluate the numerical algorithm. Extensions to the solution of other stochastic differential equations, in particular those governing the probability of failure of the linear oscillator, and applications to structural dynamics are discussed.

Original language | English (US) |
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Pages (from-to) | 345-362 |

Number of pages | 18 |

Journal | Computer Methods in Applied Mechanics and Engineering |

Volume | 27 |

Issue number | 3 |

DOIs | |

State | Published - Jul 1981 |

### ASJC Scopus subject areas

- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- Physics and Astronomy(all)
- Computer Science Applications

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## Cite this

*Computer Methods in Applied Mechanics and Engineering*,

*27*(3), 345-362. https://doi.org/10.1016/0045-7825(81)90137-7