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Solutions of Random Initial Value Problems

  • D. G. Harlow
  • T. J. Delph
Conference paper
Part of the IUTAM Symposia book series (IUTAM)

Abstract

We consider the random nonlinear initial value problem
$$ \frac{{dX}}{{dt}} = g\left( {t,X,A} \right);X\left( {{t_0}} \right) = {X_0} $$
(1)
where X = (X 1 , X 2 ,…, X n ) T , g = (g 1 , g 2 ,…, g n ) T , and T denotes transpose. The randomness in the problem arises from the vector of initial conditions X 0 = (X 1 , X 2 ,…, X n ) T , whose components are random variables with joint probability density function (jpdf) \( {f_{{{x_0}}}} \) (x 0 ), and the m random parameters A = (A 1 , A 2 ,…, A m ), which appear on the right-hand side of eqn. (1) and which have the jpdf fA (a). In general, A and X 0 may be jointly distributed; however they are often independent in many applications.

Keywords

Crack Length Random Parameter Joint Probability Density Function Jacobian Determinant Finite Element Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • D. G. Harlow
    • 1
  • T. J. Delph
    • 1
  1. 1.Lehigh UniversityBethlehemUSA

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