Random Ordinary Differential Equations and Their Numerical Solution

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...

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Main Authors: Han, Xiaoying, Kloeden, Peter E. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Published: Singapore Springer Singapore 2017, 2017
Edition:1st ed. 2017
Series:Probability Theory and Stochastic Modelling
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Table of 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