Random Ordinary Differential Equations and Their Numerical Solution

• Κύριοι συγγραφείς: Han, Xiaoying (Συγγραφέας), Kloeden, Peter E. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Singapore : Springer Singapore : Imprint: Springer, 2017.
• Σειρά: Probability Theory and Stochastic Modelling, 85
• Θέματα: Mathematics.; Numerical analysis.; Differential equations.; Probabilities.; Biomathematics.; Probability Theory and Stochastic Processes.; Numeric Computing.; Ordinary Differential Equations.; Mathematical and Computational Biology.

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...

Πίνακας περιεχομένων:

• 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.