TY  - BOOK
AU  - Griffiths,David F.
AU  - Higham,Desmond J.
ED  - SpringerLink (Online service)
TI  - Numerical Methods for Ordinary Differential Equations: Initial Value Problems 
T2  - Springer Undergraduate Mathematics Series,
SN  - 9780857291486
AV  - QA297-299.4 
U1  - 518 23
PY  - 2010///
CY  - London
PB  - Springer London
KW  - Mathematics
KW  - Electronic data processing
KW  - Numerical analysis
KW  - Numerical Analysis
KW  - Numeric Computing
N1  - 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
N2  - 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
UR  - http://148.231.10.114:2048/login?url=http://link.springer.com/book/10.1007/978-0-85729-148-6
ER  -