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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