Stochastic Ordinary Differential and Difference Equations

Chapter
Part of the Springer Series in Reliability Engineering book series (RELIABILITY)

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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Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  1. 1.Hollister HallCornell UniversityIthacaUSA

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