Research Article
Oct 1982
Numerics for Common First-Passage Problem
Publication: Journal of the Engineering Mechanics Division
Volume 108, Issue 5
Abstract
Numerical analysis aspects of the Kolmogorov backward partial differential equation associated with the first-passage problem of the response amplitude of a lightly damped linear structure are considered. It is assumed that the structure is excited by a stationary broad-band random process. A formula is presented for the analytical estimation of the eigenvalues of the boundary value problem constructed by a separation of variables procedure on the Kolmogorov equation. The analytical estimates are used as initial values in an iterative scheme which determines the eigenvalues numerically, for several values of the circular barrier of the first-passage problem. An efficient algorithm for the numerical computation of the corresponding eigenfunctions is presented. This algorithm is used, as well, to compute the constant coefficients of a solution of the Kolmogorov equation in the form of an eigenvalues-eigenfunctions series expansion. The numerical data obtained are examined in context with the physics of the problem.
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Published In
Journal of the Engineering Mechanics Division
Volume 108 • Issue 5 • October 1982
Pages: 864 - 882
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© 1982 American Society of Civil Engineers.
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Published in print: Oct 1982
Published online: Feb 3, 2021
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Polychronis-Thomas D. Spanos, M.ASCE
Assoc. Prof. of Engrg. Mechanics, Univ. of Texas, Austin, Tex. 78712
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ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.
Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.