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

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...

Full description

Saved in:
Bibliographic Details
Main Authors: Han, Xiaoying. (Author, http://id.loc.gov/vocabulary/relators/aut), Kloeden, Peter E. (http://id.loc.gov/vocabulary/relators/aut)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Singapore : Springer Singapore : Imprint: Springer, 2017.
Edition:1st ed. 2017.
Series:Probability Theory and Stochastic Modelling, 85
Springer eBook Collection.
Subjects:
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
LEADER 05293nam a22006015i 4500
001 b3278015
003 MWH
005 20191029022609.0
007 cr nn 008mamaa
008 171027s2017 si | s |||| 0|eng d
020 |a 9789811062650 
024 7 |a 10.1007/978-981-10-6265-0  |2 doi 
035 |a (DE-He213)978-981-10-6265-0 
050 4 |a E-Book 
072 7 |a PBT  |2 bicssc 
072 7 |a MAT029000  |2 bisacsh 
072 7 |a PBT  |2 thema 
072 7 |a PBWL  |2 thema 
100 1 |a Han, Xiaoying.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 0 |a Random Ordinary Differential Equations and Their Numerical Solution  |h [electronic resource] /  |c by Xiaoying Han, Peter E. Kloeden. 
250 |a 1st ed. 2017. 
264 1 |a Singapore :  |b Springer Singapore :  |b Imprint: Springer,  |c 2017. 
300 |a XVII, 250 p. 21 illus. in color.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
347 |a text file  |b PDF  |2 rda 
490 1 |a Probability Theory and Stochastic Modelling,  |x 2199-3130 ;  |v 85 
490 1 |a Springer eBook Collection 
505 0 |a 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. 
520 |a 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. . 
590 |a Loaded electronically. 
590 |a Electronic access restricted to members of the Holy Cross Community. 
650 0 |a Probabilities. 
650 0 |a Numerical analysis. 
650 0 |a Differential equations. 
650 0 |a Biomathematics. 
690 |a Electronic resources (E-books) 
700 1 |a Kloeden, Peter E.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer eBooks 
830 0 |a Probability Theory and Stochastic Modelling,  |x 2199-3130 ;  |v 85 
830 0 |a Springer eBook Collection. 
856 4 0 |u https://holycross.idm.oclc.org/login?auth=cas&url=https://doi.org/10.1007/978-981-10-6265-0  |3 Click to view e-book 
907 |a .b32780151  |b 04-18-22  |c 02-26-20 
998 |a he  |b 02-26-20  |c m  |d @   |e -  |f eng  |g si   |h 0  |i 1 
912 |a ZDB-2-SMA 
950 |a Mathematics and Statistics (Springer-11649) 
902 |a springer purchased ebooks 
903 |a SEB-COLL 
945 |f  - -   |g 1  |h 0  |j  - -   |k  - -   |l he   |o -  |p $0.00  |q -  |r -  |s b   |t 38  |u 0  |v 0  |w 0  |x 0  |y .i21911770  |z 02-26-20 
999 f f |i 73fb52b7-c652-5ed1-9e14-916c19caaebd  |s 0eeb8279-3bb7-5292-8b15-c0a97345d3f4 
952 f f |p Online  |a College of the Holy Cross  |b Main Campus  |c E-Resources  |d E-resources  |e E-Book  |h Library of Congress classification  |i Elec File  |n 1