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Numerical approximation of ordinary differential problems : from deterministic to stochastic numerical methods / Raffaela D'Ambrosio.

By: D'Ambrosio, Rafaele [author. ]Material type: Text

TextPublisher: Cham, Switzerland : Springer, c2023Description: xiv, 385 pages : illustrations (black and white)Content type: text Media type: unmediated Carrier type: volume ISBN: 9783031313424 [paperback]Subject(s): Differential problems | Counting & numeration | Mathematical analysis

Contents:

1 Ordinary differential equations -- 2 Discretization of the problem -- 3 Linear multistep methods -- 4 Rung-kutta methods -- 5 Multivalue methods -- 6 Linear stability -- 7 Stiff problems -- 8 Geometric numerical integration -- 9 Numerical methods for stochastic differential equations.

Summary: "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." --Provided by the publisher

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Item type	Current location	Call number	Status	Date due	Barcode
Subject Reference	College Annex Library Subject Reference	515.35 D18 2023 (Browse shelf)	Available		3UCBL000028719

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Previous	515 Z29 2023 Calculus II for dummies /	515.35 B78 2022 Differential equations /	515.35 C36 2024 Differential equations and applications /	515.35 D18 2023 Numerical approximation of ordinary differential problems : from deterministic to stochastic numerical methods /	515.352 M31 2018 Differential equations /	515.352 M69 2023 Differential equations /	518 C36 2023 Applied numerical methods with MATLAB for engineers and scientists /	Next

Includes bibliographical references and index.

"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." --Provided by the publisher