skip to content
Random ordinary differential equations and their numerical solution Preview this item
ClosePreview this item
Checking...

Random ordinary differential equations and their numerical solution

Author: Xiaoying Han, (Mathematician); Peter E Klon
Publisher: Singapore : Springer, 2017.
Series: Probability theory and stochastic modelling, v. 85.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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  Read more...
Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Genre/Form: Electronic books
Additional Physical Format: Print version:
Han, Xiaoying (Mathematician).
Random ordinary differential equations and their numerical solution.
Singapore : Springer, 2017
(OCoLC)994639758
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Xiaoying Han, (Mathematician); Peter E Klon
ISBN: 9789811062650 981106265X
OCLC Number: 1008868247
Description: 1 online resource
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.
Series Title: Probability theory and stochastic modelling, v. 85.
Responsibility: Xiaoying Han, Peter E. Kloeden.

Abstract:

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  Read more...

Reviews

Editorial reviews

Publisher Synopsis

"This monograph provides a general overview of random ordinary differential equations (RODEs) with emphasis on numerical methods used to solve them. ... This book is a welcome addition to the Read more...

 
User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.
Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


Primary Entity

<http://www.worldcat.org/oclc/1008868247> # Random ordinary differential equations and their numerical solution
    a schema:CreativeWork, schema:Book, schema:MediaObject ;
    library:oclcnum "1008868247" ;
    library:placeOfPublication <http://id.loc.gov/vocabulary/countries/si> ;
    schema:about <http://experiment.worldcat.org/entity/work/data/4567230036#Topic/differential_equations_numerical_solutions> ; # Differential equations--Numerical solutions
    schema:about <http://experiment.worldcat.org/entity/work/data/4567230036#Topic/probability_&_statistics> ; # Probability & statistics
    schema:about <http://experiment.worldcat.org/entity/work/data/4567230036#Topic/mathematics_numerical_analysis> ; # MATHEMATICS--Numerical Analysis
    schema:about <http://experiment.worldcat.org/entity/work/data/4567230036#Topic/mathematical_theory_of_computation> ; # Mathematical theory of computation
    schema:about <http://experiment.worldcat.org/entity/work/data/4567230036#Topic/maths_for_scientists> ; # Maths for scientists
    schema:about <http://dewey.info/class/518.63/e23/> ;
    schema:about <http://experiment.worldcat.org/entity/work/data/4567230036#Topic/differential_calculus_&_equations> ; # Differential calculus & equations
    schema:author <http://experiment.worldcat.org/entity/work/data/4567230036#Person/klon_peter_e> ; # Peter E. Klon
    schema:author <http://experiment.worldcat.org/entity/work/data/4567230036#Person/han_xiaoying_mathematician> ; # (Mathematician) Xiaoying Han
    schema:bookFormat schema:EBook ;
    schema:datePublished "2017" ;
    schema:description "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. .--"@en ;
    schema:description "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."@en ;
    schema:exampleOfWork <http://worldcat.org/entity/work/id/4567230036> ;
    schema:genre "Electronic books"@en ;
    schema:inLanguage "en" ;
    schema:isPartOf <http://worldcat.org/issn/2199-3130> ; # Probability theory and stochastic modelling,
    schema:isPartOf <http://experiment.worldcat.org/entity/work/data/4567230036#Series/probability_theory_and_stochastic_modelling> ; # Probability theory and stochastic modelling ;
    schema:isSimilarTo <http://www.worldcat.org/oclc/994639758> ;
    schema:name "Random ordinary differential equations and their numerical solution"@en ;
    schema:productID "1008868247" ;
    schema:url <https://0-link-springer-com.pugwash.lib.warwick.ac.uk/book/10.1007/978-981-10-6265-0> ;
    schema:url <https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=1623550> ;
    schema:url <http://rave.ohiolink.edu/ebooks/ebc/9789811062650> ;
    schema:url <https://link.springer.com/openurl?genre=book&isbn=978-981-10-6264-3> ;
    schema:url <https://doi.org/10.1007/978-981-10-6265-0> ;
    schema:url <http://www.vlebooks.com/vleweb/product/openreader?id=none&isbn=9789811062650> ;
    schema:url <http://public.ebookcentral.proquest.com/choice/publicfullrecord.aspx?p=5115922> ;
    schema:url <https://link.springer.com/10.1007/978-981-10-6265-0> ;
    schema:url <http://link.springer.com/10.1007/978-981-10-6265-0> ;
    schema:url <https://0-link-springer-com.pugwash.lib.warwick.ac.uk/10.1007/978-981-10-6265-0> ;
    schema:workExample <http://dx.doi.org/10.1007/978-981-10-6265-0> ;
    schema:workExample <http://worldcat.org/isbn/9789811062650> ;
    umbel:isLike <http://bnb.data.bl.uk/id/resource/GBB8I4556> ;
    wdrs:describedby <http://www.worldcat.org/title/-/oclc/1008868247> ;
    .


Related Entities

<http://experiment.worldcat.org/entity/work/data/4567230036#Person/han_xiaoying_mathematician> # (Mathematician) Xiaoying Han
    a schema:Person ;
    schema:familyName "Han" ;
    schema:givenName "Xiaoying" ;
    schema:name "(Mathematician) Xiaoying Han" ;
    .

<http://experiment.worldcat.org/entity/work/data/4567230036#Person/klon_peter_e> # Peter E. Klon
    a schema:Person ;
    schema:familyName "Klon" ;
    schema:givenName "Peter E." ;
    schema:name "Peter E. Klon" ;
    .

<http://experiment.worldcat.org/entity/work/data/4567230036#Series/probability_theory_and_stochastic_modelling> # Probability theory and stochastic modelling ;
    a bgn:PublicationSeries ;
    schema:hasPart <http://www.worldcat.org/oclc/1008868247> ; # Random ordinary differential equations and their numerical solution
    schema:name "Probability theory and stochastic modelling ;" ;
    .

<http://experiment.worldcat.org/entity/work/data/4567230036#Topic/differential_calculus_&_equations> # Differential calculus & equations
    a schema:Intangible ;
    schema:name "Differential calculus & equations"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/4567230036#Topic/differential_equations_numerical_solutions> # Differential equations--Numerical solutions
    a schema:Intangible ;
    schema:name "Differential equations--Numerical solutions"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/4567230036#Topic/mathematical_theory_of_computation> # Mathematical theory of computation
    a schema:Intangible ;
    schema:name "Mathematical theory of computation"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/4567230036#Topic/mathematics_numerical_analysis> # MATHEMATICS--Numerical Analysis
    a schema:Intangible ;
    schema:name "MATHEMATICS--Numerical Analysis"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/4567230036#Topic/maths_for_scientists> # Maths for scientists
    a schema:Intangible ;
    schema:name "Maths for scientists"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/4567230036#Topic/probability_&_statistics> # Probability & statistics
    a schema:Intangible ;
    schema:name "Probability & statistics"@en ;
    .

<http://worldcat.org/isbn/9789811062650>
    a schema:ProductModel ;
    schema:isbn "981106265X" ;
    schema:isbn "9789811062650" ;
    .

<http://worldcat.org/issn/2199-3130> # Probability theory and stochastic modelling,
    a bgn:PublicationSeries ;
    schema:hasPart <http://www.worldcat.org/oclc/1008868247> ; # Random ordinary differential equations and their numerical solution
    schema:issn "2199-3130" ;
    schema:name "Probability theory and stochastic modelling," ;
    .

<http://www.worldcat.org/oclc/994639758>
    a schema:CreativeWork ;
    rdfs:label "Random ordinary differential equations and their numerical solution." ;
    schema:description "Print version:" ;
    schema:isSimilarTo <http://www.worldcat.org/oclc/1008868247> ; # Random ordinary differential equations and their numerical solution
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.