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

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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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© 1971 Springer-Verlag

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Huss, R., Kalaba, R. (1971). Computation of the moments of solutions of certain random two point boundary value problems. In: Morris, J.L. (eds) Conference on Applications of Numerical Analysis. Lecture Notes in Mathematics, vol 228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069451

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  • DOI: https://doi.org/10.1007/BFb0069451

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05656-0

  • Online ISBN: 978-3-540-36976-9

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