Sign in
Author

Conference

Journal

Organization

Year

DOI
Look for results that meet for the following criteria:
since
equal to
before
between
and
Search in all fields of study
Limit my searches in the following fields of study
Agriculture Science
Arts & Humanities
Biology
Chemistry
Computer Science
Economics & Business
Engineering
Environmental Sciences
Geosciences
Material Science
Mathematics
Medicine
Physics
Social Science
Multidisciplinary
Keywords
(3)
Ordinary Differential Equation
Random Parameters
Spectral Method
Subscribe
Academic
Publications
NUMERICS OF THE VANDERPOL EQUATION WITH RANDOM PARAMETER
NUMERICS OF THE VANDERPOL EQUATION WITH RANDOM PARAMETER,F. Augustin,P. Rentrop
Edit
NUMERICS OF THE VANDERPOL EQUATION WITH RANDOM PARAMETER
BibTex

RIS

RefWorks
Download
F. Augustin
,
P. Rentrop
In this article, the problem of longterm integration in the WienerHermite calculus for ordinary differential equations with
random parameters
is discussed. The WienerHermite calculus is known to lose accuracy with increasing time, even if it provides good results for short times. This is demonstrated for the VanderPol equation with a random parameter. To reduce this problem, the adapted stochastic
spectral method
(aSSM), which is based on the work of P. Vos (8), is presented. Applying aSSM to the VanderPol equation reduces the error considerably and allows an accurate longterm integration.
Cumulative
Annual
View Publication
The following links allow you to view full publications. These links are maintained by other sources not affiliated with Microsoft Academic Search.
(
www.unige.ch
)
References
(13)
Stochastic Finite Elements: A Spectral Approach
(
Citations: 1000
)
P. Spanos
Published in 1991.
An adaptive multielement generalized polynomial chaos method for stochastic differential equations
(
Citations: 98
)
Xiaoliang Wan
,
George Em. Karniadakis
Journal:
Journal of Computational Physics  J COMPUT PHYS
, vol. 209, no. 2, pp. 617642, 2005
Efficient Collocational Approach for Parametric Uncertainty Analysis
(
Citations: 61
)
Dongbin Xiu
The WienerAskey polynomial chaos for stochastic di erential equations
(
Citations: 96
)
D. Xiu
,
G. E. Karniadakis
Journal:
Siam Journal on Scientific Computing
, 2002
Solving ordinary differential equations ii
(
Citations: 1112
)
E. Hairer
,
G. Wanner
Published in 1996.