文档介绍：This page intentionally left blank
A First Course in the Numerical Analysis
of Differential Equations
Numerical analysis presents different faces to the world. For mathematicians it is a bona fide
mathematical theory with an applicable flavour. For scientists and engineers it is a practical,
applied subject, part of the standard repertoire of modelling techniques. puter
scientists it is a theory on the interplay puter architecture and algorithms for real-
number calculations.
The tension between these standpoints is the driving force of this book, which presents
a rigorous account of the fundamentals of numerical analysis both of ordinary and partial
differential equations. The point of departure is mathematical, but the exposition strives to
maintain a balance among theoretical, algorithmic and applied aspects of the subject.
This new edition has been extensively updated, and includes new chapters on developing
subject areas: geometric numerical integration, an emerging paradigm for numerical
computation that exhibits exact conservation of important geometric and structural features
of the underlying differential equation; spectral methods, which e to be seen in
the last two decades as a petitor to finite differences and finite elements; and
conjugate gradients, one of the most powerful contemporary tools in the solution of sparse
linear algebraic systems.
Other topics covered include numerical solution of ordinary differential equations by
multistep and Runge–Kutta methods; finite difference and finite elements techniques for
the Poisson equation; a variety of algorithms to solve large, sparse algebraic systems;
methods for parabolic and hyperbolic differential equations and techniques for their
analysis. The book is panied by an appendix that presents brief back-up in a number
of mathematical topics.
Professor Iserles concentrates on fundamentals: deriving methods from first principles,
analysing them with a variety of mathematical techniqu