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Erschienen in:
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2012 | OriginalPaper | Buchkapitel

7. Stochastic Ordinary Differential and Difference Equations

verfasst von : Mircea Grigoriu

Erschienen in: Stochastic Systems

Verlag: Springer London

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Abstract

Summary Methods are developed for solving ordinary differential and difference equations with random coefficients and/or input. Following an introductory section (Sect. 1), we present methods for solving equations with deterministic coefficients and random input (Sect. 2), finite difference equations with random coefficients of arbitrary and small uncertainty (Sect. 3), and ordinary differential equations with random coefficients of arbitrary and small uncertainty (Sect. 4). The methods include Monte Carlo simulation, conditional analysis, stochastic reduced order models, stochastic Galerkin, stochastic collocation, Taylor series, and Neumann series. Applications from stochastic stability, noise induced transitions, random vibration, and reliability of degrading systems conclude the chapter (Sect. 5).

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Vorheriges Kapitel Probabilistic Models
Nächstes Kapitel Stochastic Algebraic Equations
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Metadaten
Titel
Stochastic Ordinary Differential and Difference Equations
verfasst von
Mircea Grigoriu
Copyright-Jahr
2012
Verlag
Springer London
Buch
Stochastic Systems

Print ISBN: 978-1-4471-2326-2

Electronic ISBN: 978-1-4471-2327-9

Copyright-Jahr: 2012

DOI
https://doi.org/10.1007/978-1-4471-2327-9_7