A First Course in the Numerical Analysis of Differential Equations

Front Cover
Cambridge University Press, 2009 - Mathematics - 459 pages
1 Review
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. For computer scientists it is a theory on the interplay of computer 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 of both ordinary and partial differential equations. The exposition maintains a balance between theoretical, algorithmic and applied aspects. This new edition has been extensively updated, and includes new chapters on emerging subject areas: geometric numerical integration, spectral methods and conjugate gradients. Other topics covered include multistep and Runge-Kutta methods; finite difference and finite elements techniques for the Poisson equation; and a variety of algorithms to solve large, sparse algebraic systems.
  

What people are saying - Write a review

We haven't found any reviews in the usual places.

Related books

Contents

Multistep methods
19
RungeKutta methods
33
Stiff equations
53
Geometric numerical integration
73
Error control
105
Nonlinear algebraic systems
123
Finite difference schemes
139
The finite element method
171
Classical iterative methods for sparse linear equations
251
Multigrid techniques
291
Conjugate gradients
309
Fast Poisson solvers
331
The diffusion equation
349
Hyperbolic equations
387
Appendix Bluffers guide to useful mathematics
427
Index
447

Spectral methods
205
Gaussian elimination for sparse linear equations
233

Other editions - View all

Common terms and phrases

About the author (2009)

Arieh Iserles is a Professor in Numerical Analysis of Differential Equations in the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge. He has been awarded the Onsager medal and served as a chair of the Society for Foundations of Computational Mathematics. He is also Managing Editor of Acta Numerica, Editor in Chief of Foundations of Computational Mathematics, and an editor of numerous other publications.

Bibliographic information