Griffiths / Higham Numerical Methods for Ordinary Differential Equations

Initial Value Problems
1. Auflage 2010
ISBN: 978-0-85729-148-6
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 271 Seiten, eBook

Reihe: Springer Undergraduate Mathematics Series

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 methodso Runge--Kutta methodso Linear multistep methodso Convergenceo Stabilityand a range of modern themes:o Adaptive stepsize selectiono Long term dynamicso Modified equationso Geometric integrationo Stochastic differential equationsThe 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

Zielgruppe

Lower undergraduate

Autoren/Hrsg.

Griffiths, David F.

Higham, Desmond J.

Inhaltsverzeichnis

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.