Stochastic Ordinary Differential and Difference Equations

Mircea Grigoriu ()
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Mircea Grigoriu: Cornell University

Chapter Chapter 7 in Stochastic Systems, 2012, pp 237-335 from Springer

Abstract: 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).

Keywords: Stochastic Reduced Order Models (SROMs); Stochastic Galerkin; Random Coefficients; Stochastic Differential Equations (SDEs); Stochastic Collocation Method (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-1-4471-2327-9_7

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