Numerical Methods for Ordinary Differential Equations
Initial Value Problems
Series: Springer Undergraduate Mathematics Series;
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Product details:
- Edition number 2010
- Publisher Springer London
- Date of Publication 25 November 2010
- Number of Volumes 1 pieces, Book
- ISBN 9780857291479
- Binding Paperback
- No. of pages271 pages
- Size 235x155 mm
- Weight 900 g
- Language English
- Illustrations XIV, 271 p. 69 illus. Illustrations, black & white 0
Categories
Long description:
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
MoreTable of Contents:
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.
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