Petrov-Galerkin finite element solution for the first passage probability and moments of first passage time of the randomly accelerated free particle

Lawrence Bergman, J. C. Heinrich

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)345-362
Number of pages18
JournalComputer Methods in Applied Mechanics and Engineering
Volume27
Issue number3
DOIs
StatePublished - Jul 1981

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moments
dynamic structural analysis
Structural dynamics
boundary value problems
Boundary value problems
finite element method
Differential equations
differential equations
oscillators
Finite element method

ASJC Scopus subject areas

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

Cite this

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