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Computation of the moments of solutions of certain random two point boundary value problems

  • R. Huss
  • R. Kalaba
Invited Papers
Part of the Lecture Notes in Mathematics book series (LNM, volume 228)

Abstract

Assume that the linear two-point boundary value problem
$$\begin{gathered}\mathop x\limits^\infty + [p(t) + \lambda q(t)]x = - g(t),0 \leqslant t \leqslant 1, \hfill \\x(0) = 0,x(1) = c \hfill \\\end{gathered}$$
possesses a unique solution for all λ in the interval 0 ≤ λ ≤ Λ. Consider λ to be a random variable with probability density function f(λ), 0 ≤ λ ≤ Λ. A method for determining the moments
$$\begin{gathered}E[x^n (t,\lambda )] = \int_0^\Lambda {x^n (t,\lambda )f(\lambda )d\lambda } , \hfill \\n = 1,2, \cdots , \hfill \\\end{gathered}$$
is presented. Numerical experiments show the computational feasibility of the new approach.

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Copyright information

© Springer-Verlag 1971

Authors and Affiliations

  • R. Huss
  • R. Kalaba

There are no affiliations available

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