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The Resource Random Ordinary Differential Equations and Their Numerical Solution, by Xiaoying Han, Peter E. Kloeden, (electronic resource)

Random Ordinary Differential Equations and Their Numerical Solution, by Xiaoying Han, Peter E. Kloeden, (electronic resource)

Label
Random Ordinary Differential Equations and Their Numerical Solution
Title
Random Ordinary Differential Equations and Their Numerical Solution
Statement of responsibility
by Xiaoying Han, Peter E. Kloeden
Creator
Contributor
Author
Subject
Language
eng
Summary
This book is intended to make recent results on the derivation of higher order numerical schemes for random ordinary differential equations (RODEs) available to a broader readership, and to familiarize readers with RODEs themselves as well as the closely associated theory of random dynamical systems. In addition, it demonstrates how RODEs are being used in the biological sciences, where non-Gaussian and bounded noise are often more realistic than the Gaussian white noise in stochastic differential equations (SODEs). RODEs are used in many important applications and play a fundamental role in the theory of random dynamical systems. They can be analyzed pathwise with deterministic calculus, but require further treatment beyond that of classical ODE theory due to the lack of smoothness in their time variable. Although classical numerical schemes for ODEs can be used pathwise for RODEs, they rarely attain their traditional order since the solutions of RODEs do not have sufficient smoothness to have Taylor expansions in the usual sense. However, Taylor-like expansions can be derived for RODEs using an iterated application of the appropriate chain rule in integral form, and represent the starting point for the systematic derivation of consistent higher order numerical schemes for RODEs. The book is directed at a wide range of readers in applied and computational mathematics and related areas as well as readers who are interested in the applications of mathematical models involving random effects, in particular in the biological sciences.The level of this book is suitable for graduate students in applied mathematics and related areas, computational sciences and systems biology. A basic knowledge of ordinary differential equations and numerical analysis is required. .--
Member of
Assigning source
Provided by publisher
http://library.link/vocab/creatorName
Han, Xiaoying
Image bit depth
0
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
Kloeden, Peter E.
Series statement
  • Springer eBooks
  • Probability Theory and Stochastic Modelling,
Series volume
85
http://library.link/vocab/subjectName
  • Mathematics
  • Numerical analysis
  • Differential equations
  • Probabilities
  • Biomathematics
Label
Random Ordinary Differential Equations and Their Numerical Solution, by Xiaoying Han, Peter E. Kloeden, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-981-10-6265-0
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Preface -- Reading Guide -- Part I Random and Stochastic Ordinary Differential Equations -- 1.Introduction.-. 2.Random ordinary differential equations -- 3.Stochastic differential equations -- 4.Random dynamical systems -- 5.Numerical dynamics -- Part II Taylor Expansions -- 6.Taylor expansions for ODEs and SODEs -- 7.Taylor expansions for RODEs with affine noise -- 8.Taylor expansions for general RODEs -- Part III Numerical Schemes for Random Ordinary Differential Equations -- 9.Numerical methods for ODEs and SODEs -- 10.Numerical schemes: RODEs with Itô noise -- 11.Numerical schemes: affine noise -- 12.RODE–Taylor schemes -- 13.Numerical stability -- 14.Stochastic integrals -- Part IV Random Ordinary Differential Equations in the Life Sciences -- 15.Simulations of biological systems -- 16.Chemostat -- 17.Immune system virus model -- 18.Random Markov chains -- Part V Appendices -- A.Probability spaces -- B.Chain rule for affine RODEs -- C.Fractional Brownian motion -- References -- Index
Control code
978-981-10-6265-0
Dimensions
unknown
Extent
1 online resource (XVII, 250 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9789811062650
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-981-10-6265-0
Other physical details
21 illustrations in color.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1008868247
Label
Random Ordinary Differential Equations and Their Numerical Solution, by Xiaoying Han, Peter E. Kloeden, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-981-10-6265-0
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Preface -- Reading Guide -- Part I Random and Stochastic Ordinary Differential Equations -- 1.Introduction.-. 2.Random ordinary differential equations -- 3.Stochastic differential equations -- 4.Random dynamical systems -- 5.Numerical dynamics -- Part II Taylor Expansions -- 6.Taylor expansions for ODEs and SODEs -- 7.Taylor expansions for RODEs with affine noise -- 8.Taylor expansions for general RODEs -- Part III Numerical Schemes for Random Ordinary Differential Equations -- 9.Numerical methods for ODEs and SODEs -- 10.Numerical schemes: RODEs with Itô noise -- 11.Numerical schemes: affine noise -- 12.RODE–Taylor schemes -- 13.Numerical stability -- 14.Stochastic integrals -- Part IV Random Ordinary Differential Equations in the Life Sciences -- 15.Simulations of biological systems -- 16.Chemostat -- 17.Immune system virus model -- 18.Random Markov chains -- Part V Appendices -- A.Probability spaces -- B.Chain rule for affine RODEs -- C.Fractional Brownian motion -- References -- Index
Control code
978-981-10-6265-0
Dimensions
unknown
Extent
1 online resource (XVII, 250 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9789811062650
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-981-10-6265-0
Other physical details
21 illustrations in color.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1008868247

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