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Proceedings Paper

Dynamics of linearly partial-implicit midpoint methods for numerical integration of some infinite systems of ODEs with cubic-type nonlinearity and Q-regular additive noise
Author(s): Henri Schurz
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Paper Abstract

Qualitative aspects of numerical methods for integration of systems of nonlinear ordinary stochastic differential equations (SDEs) with potential applicability to mechanical engineering are presented. In particular, we study the qualitative behavior of some linearly partial-implicit midpoint-type methods for numerical integration of infinite and finite systems of SDEs with cubic-type nonlinearity and Q-regular additive space-time noise. Construction and properties such as stability and convergence of such stochastic-numerical methods is strongly related to their uniform boundedness along Lyapunov-type functionals. Well-known convergence order bounds apart from further complexity issues forces us to focus our analysis on lower order Runge-Kutta methods rather than higher order Taylor methods. Nonstandard techniques such as partial-implicit difference methods for noisy ODEs/PDEs seem to be the most promising ones in view of adequate longterm integration of such nonlinear systems.

Paper Details

Date Published: 23 May 2005
PDF: 11 pages
Proc. SPIE 5845, Noise in Complex Systems and Stochastic Dynamics III, (23 May 2005);
Show Author Affiliations
Henri Schurz, Southern Illinois Univ. (United States)
Texas Tech Univ. (United States)

Published in SPIE Proceedings Vol. 5845:
Noise in Complex Systems and Stochastic Dynamics III
Laszlo B. Kish; Katja Lindenberg; Zoltan Gingl, Editor(s)

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