Numerical Approximation of Ordinary Differential Problems: From Deterministic to Stochastic Numerical Methods: 148 (UNITEXT, 148) - Softcover

D'Ambrosio, Raffaele

 
9783031313424: Numerical Approximation of Ordinary Differential Problems: From Deterministic to Stochastic Numerical Methods: 148 (UNITEXT, 148)
Softcover
ISBN 10: 3031313429 ISBN 13: 9783031313424
Publisher: Springer, 2023

Synopsis

This book is focused on the numerical discretization of ordinary differential equations (ODEs), under several perspectives. The attention is first conveyed to providing accurate numerical solutions of deterministic problems. Then, the presentation moves to a more modern vision of numerical approximation, oriented to reproducing qualitative properties of the continuous problem along the discretized dynamics over long times. The book finally performs some steps in the direction of stochastic differential equations (SDEs), with the intention of offering useful tools to generalize the techniques introduced for the numerical approximation of ODEs to the stochastic case, as well as of presenting numerical issues natively introduced for SDEs.


The book is the result of an intense teaching experience as well as of the research carried out in the last decade by the author. It is both intended for students and instructors: for the students, this book is comprehensive and ratherself-contained; for the instructors, there is material for one or more monographic courses on ODEs and related topics. In this respect, the book can be followed in its designed path and includes motivational aspects, historical background, examples and a software programs, implemented in Matlab, that can be useful for the laboratory part of a course on numerical ODEs/SDEs.

The book also contains the portraits of several pioneers in the numerical discretization of differential problems, useful to provide a framework to understand their contributes in the presented fields. Last, but not least, rigor joins readability in the book.

"synopsis" may belong to another edition of this title.

About the Author

Raffaele D'Ambrosio is Full Professor of Numerical Analysis at the University of L'Aquila. He got his Ph.D. in Mathematics in 2006, by a joint program between the University of Salerno and Arizona State University. In 2011 he has been awarded with Galileo Galilei Prize for young researchers. In 2014 he has been Fulbright Research Scholar at Georgia Institute of Technology. His main research interests regard structure-preserving approximation of deterministic and stochastic evolutive problems.

From the Back Cover

This book is focused on the numerical discretization of ordinary differential equations (ODEs), under several perspectives. The attention is first conveyed to providing accurate numerical solutions of deterministic problems. Then, the presentation moves to a more modern vision of numerical approximation, oriented to reproducing qualitative properties of the continuous problem along the discretized dynamics over long times. The book finally performs some steps in the direction of stochastic differential equations (SDEs), with the intention of offering useful tools to generalize the techniques introduced for the numerical approximation of ODEs to the stochastic case, as well as of presenting numerical issues natively introduced for SDEs.


The book is the result of an intense teaching experience as well as of the research carried out in the last decade by the author. It is both intended for students and instructors: for the students, this book is comprehensive and ratherself-contained; for the instructors, there is material for one or more monographic courses on ODEs and related topics. In this respect, the book can be followed in its designed path and includes motivational aspects, historical background, examples and a software programs, implemented in Matlab, that can be useful for the laboratory part of a course on numerical ODEs/SDEs.

The book also contains the portraits of several pioneers in the numerical discretization of differential problems, useful to provide a framework to understand their contributes in the presented fields. Last, but not least, rigor joins readability in the book.

"About this title" may belong to another edition of this title.

Publisher
Springer
Publication date
2023
Language
English
ISBN 10 
3031313429
ISBN 13 
9783031313424
Binding
Paperback
Edition number
1
Number of pages
399