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Modelling with Ordinary Differential Equations

Alfio Borzì
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A01=Alfio Borzi
applied mathematics
Author_Alfio Borzi
boundary value problems
calculus of variations
Category=PBKJ
Category=PBKS
Category=PBWH
Cauchy Problem
Conditional PDF
control theory applications
Differential Riccati Equation
eigenvalue analysis
Em Approximation
Em Scheme
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Euler's method
Finite-dimensional spaces
Green's Function
Green’s Function
Hamiltonian systems
Infinite-dimensional spaces
Inverse Problems
Inverse Source Problem
Linear Homogeneous Ode
Linear Quadratic Differential Games
mathematical modeling
MLP Network
Ne Point
neural network ODE solutions
Non-trivial Solutions
Numerical integration
Ode Model
Open Loop NE
Optimal Control Problems
Order Ode
Ordinary Differential Equations
Parameter Identification Problem
Pareto Front
PO Point
SDE
stability analysis
Stochastic differential equations
Sturm Liouville Operator
Sturm Liouville Problem
teaching material
The Lagrange framework
The Lorenz model
Weak Local Minimiser

Product details

  • ISBN 9780815392613
  • Weight: 453g
  • Dimensions: 156 x 234mm
  • Publication Date: 07 Apr 2020
  • Publisher: Taylor & Francis Inc
  • Publication City/Country: US
  • Product Form: Hardback
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Description

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
About Alfio Borzi

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.

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