Başlık:
Numerical Methods for Ordinary Differential Equations Initial Value Problems
Dil:
English
ISBN:
9780857291486
Yayın Bilgileri:
London : Springer London, 2010.
Fiziksel Tanımlama:
XIV, 271 p. 69 illus. online resource.
Seri:
İçerik:
ODEs—An Introduction -- Euler’s Method -- The Taylor Series Method -- Linear Multistep Methods—I: Construction and Consistency -- Linear Multistep Methods—II: Convergence and Zero-Stability -- Linear Multistep Methods—III: Absolute Stability -- Linear Multistep Methods—IV: Systems of ODEs -- Linear Multistep Methods—V: Solving Implicit Methods -- Runge–Kutta Method—I: Order Conditions -- Runge-Kutta Methods–II Absolute Stability -- Adaptive Step Size Selection -- Long-Term Dynamics -- Modified Equations -- Geometric Integration Part I—Invariants -- Geometric Integration Part II—Hamiltonian Dynamics -- Stochastic Differential Equations.
Özet:
Numerical Methods for Ordinary Differential Equations is a self-contained introduction to a fundamental field of numerical analysis and scientific computation. Written for undergraduate students with a mathematical background, this book focuses on the analysis of numerical methods without losing sight of the practical nature of the subject. It covers the topics traditionally treated in a first course, but also highlights new and emerging themes. Chapters are broken down into `lecture' sized pieces, motivated and illustrated by numerous theoretical and computational examples. Over 200 exercises are provided and these are starred according to their degree of difficulty. Solutions to all exercises are available to authorized instructors. The book covers key foundation topics: o Taylor series methods o Runge-Kutta methods o Linear multistep methods o Convergence o Stability and a range of modern themes: o Adaptive stepsize selection o Long term dynamics o Modified equations o Geometric integration o Stochastic differential equations The prerequisite of a basic university-level calculus class is assumed, although appropriate background results are also summarized in appendices. A dedicated website for the book containing extra information can be found via www.springer.com.

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### Özet

Numerical Methods for Ordinary Differential Equations is a self-contained introduction to a fundamental field of numerical analysis and scientific computation. Written for undergraduate students with a mathematical background, this book focuses on the analysis of numerical methods without losing sight of the practical nature of the subject.

It covers the topics traditionally treated in a first course, but also highlights new and emerging themes. Chapters are broken down into `lecture' sized pieces, motivated and illustrated by numerous theoretical and computational examples.

Over 200 exercises are provided and these are starred according to their degree of difficulty. Solutions to all exercises are available to authorized instructors.

The book covers key foundation topics:

o Taylor series methods

o Runge--Kutta methods

o Linear multistep methods

o Convergence

o Stability

and a range of modern themes:

o Long term dynamics

o Modified equations

o Geometric integration

o Stochastic differential equations

The prerequisite of a basic university-level calculus class is assumed, although appropriate background results are also summarized in appendices. A dedicated website for the book containing extra information can be found via www.springer.com

### İnceleme Seç

This book by Griffiths (Univ. of Dundee, UK) and Higham (Univ. of Strathclyde, UK) introduces the fields of numerical analysis and scientific computation. Traditional ordinary differential equations courses teach the basic theory behind the subject, which often limits its practical value in solving realistic mathematical models. The focus of this book is the computational methods that give approximate solutions to such models. The authors write, "The main aim of this book is to give students an understanding of what goes on 'under the hood' in scientific computing software...." The topics discussed cover both typical areas, for example, Euler's method, Taylor series methods, Runge-Kutta methods, convergence, and stability, and more current material such as stochastic differential equations, long-term dynamics, and geometric integration. Overall, there are many examples and exercises for students to read and try. There are no hints or solutions in the back of the book for the exercises, but instructors can obtain a complete solution set from the book's Web site. The work is very readable for an introductory course. An undergraduate who has completed at least the full calculus sequence should find the material interesting and accessible. Summing Up: Recommended. Lower-division undergraduates. S. L. Sullivan Catawba College