Modelling with Ordinary Differential Equations

A Comprehensive Approach
1. Auflage 2020
ISBN: 978-0-8153-9261-3
Verlag: CRC Press

Buch, Englisch, 404 Seiten, Format (B × H): 160 mm x 239 mm, Gewicht: 680 g

Reihe: Chapman & Hall/CRC Numerical Analysis and Scientific Computing Series

Modelling with Ordinary Differential Equations: A Comprehensive Approach aims to provide a broad and self-contained introduction to the mathematical tools necessary to investigate and apply ODE models. The book starts by establishing the existence of solutions in various settings and analysing their stability properties. The next step is to illustrate modelling issues arising in the calculus of variation and optimal control theory that are of interest in many applications. This discussion is continued with an introduction to inverse problems governed by ODE models and to differential games.

The book is completed with an illustration of stochastic differential equations and the development of neural networks to solve ODE systems. Many numerical methods are presented to solve the classes of problems discussed in this book.

Features:

- Provides insight into rigorous mathematical issues concerning various topics, while discussing many different models of interest in different disciplines (biology, chemistry, economics, medicine, physics, social sciences, etc.)

- Suitable for undergraduate and graduate students and as an introduction for researchers in engineering and the sciences

- Accompanied by codes which allow the reader to apply the numerical methods discussed in this book in those cases where analytical solutions are not available

Autoren/Hrsg.

Borzì, Alfio

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Technische Wissenschaften Technik Allgemein Technik: Allgemeines
• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

1. Introduction. 2. Elementary solution methods for simple ODEs. 3. Theory of ordinary differential equations. 4. Systems of ordinary differentail equations. 5. Ordinary differential equations of order n. 6. Stability of ODE systems. 7. Boundary and eigenvalue problems. 8. Numerical solution of ODE problems. 9. ODEs and the calculus of variations. 10. Optimal control of ODE models. 11. Inverse problems with ODE models. 12. Differential games. 13. Stochastic differential equations. 14. Neural networks and ODE problems.

Über Autor(innen)

Alfio Borzì, born 1965 in Catania (Italy), is the professor and chair of Scientific Computing at the Institute for Mathematics of the University of Würzburg, Germany. He studied Mathematics and Physics in Catania and Trieste where he received his PhD in Mathematics from Scuola Internazionale Superiore di Studi Avanzati (SISSA).

He served as Research Officer at the University of Oxford (UK) and as assistant professor at the University of Graz (Austria) where he completed his Habilitation and was appointed as Associate Professor. Since 2011 he has been Professor of Scientific Computing at University of Würzburg.

Alfio Borzi is the author of 3 mathematics books and numerous articles in journals. The main topics of his research and teaching activities are modelling and numerical analysis, optimal control theory and scientific computing. He is member of the editorial board for the SIAM Journal on
Scientific Computing and for SIAM Review.