Overview
- Makes recent results on the derivation of higher order numerical schemes for random ordinary differential equations (RODEs) available to a broader readership
- Develops numerical methods for random ODEs (RODEs)
- Highlights important applications, with a focus on dynamical behavior and the biological sciences
- Includes supplementary material: sn.pub/extras
Part of the book series: Probability Theory and Stochastic Modelling (PTSM, volume 85)
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Table of contents (18 chapters)
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Front Matter
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Random and Stochastic Ordinary Differential Equations
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Front Matter
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Numerical Schemes for Random Ordinary Differential Equations
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Front Matter
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Random Ordinary Differential Equations in the Life Sciences
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Front Matter
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Keywords
About this book
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.
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Authors and Affiliations
About the authors
Professor Xiaoying Han’s main research interests are in random and nonautonomous dynamical systems and their applications. In addition to mathematical analysis of dynamical systems, she is also interested in modeling and simulation of applied dynamical systems in biology, chemical engineering, ecology, material sciences, etc. She is the coauthor of the books “Applied Nonautonomous and Random Dynamical Systems” (with T. Caraballo) and “Attractors under Discretisation” (with P. E. Kloeden), published in the SpringerBrief series.
Bibliographic Information
Book Title: Random Ordinary Differential Equations and Their Numerical Solution
Authors: Xiaoying Han, Peter E. Kloeden
Series Title: Probability Theory and Stochastic Modelling
DOI: https://doi.org/10.1007/978-981-10-6265-0
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Singapore Pte Ltd. 2017
Hardcover ISBN: 978-981-10-6264-3Published: 08 November 2017
Softcover ISBN: 978-981-13-4843-3Published: 11 December 2018
eBook ISBN: 978-981-10-6265-0Published: 25 October 2017
Series ISSN: 2199-3130
Series E-ISSN: 2199-3149
Edition Number: 1
Number of Pages: XVII, 250
Number of Illustrations: 21 illustrations in colour
Topics: Probability Theory and Stochastic Processes, Numeric Computing, Ordinary Differential Equations, Mathematical and Computational Biology