A First Course in the Numerical Analysis of Differential Equations

by Arieh Iserles

Overview

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 second 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.

Product Details

ISBN-13:	9781139636568
Publisher:	Cambridge University Press
Publication date:	11/27/2008
Series:	Cambridge Texts in Applied Mathematics , #44
Sold by:	Barnes & Noble
Format:	eBook
File size:	29 MB
Note:	This product may take a few minutes to download.

About the Author

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.

Table of Contents

Preface to the first edition; Preface to the second edition; Flowchart of contents; Part I. Ordinary Differential Equations: 1. Euler's method and beyond; 2. Multistep methods; 3. Runge–Kutta methods; 4. Stiff equations; 5. Geometric numerical integration; 6. Error control; 7. Nonlinear algebraic systems; Part II. The Poisson Equation: 8. Finite difference schemes; 9. The finite element method; 10. Spectral methods; 11. Gaussian elimination for sparse linear equations; 12. Classical iterative methods for sparse linear equations; 13. Multigrid techniques; 14. Conjugate gradients; 15. Fast Poisson solvers; Part III. Partial Differential Equations of evolution: 16. The diffusion equation; 17. Hyperbolic equations; Appendix. Bluffer's guide to useful mathematics: A.1. Linear algebra; A.2. Analysis; Bibliography; Index.

What People are Saying About This

From the Publisher

'A well written and exciting book … the exposition throughout is clear and very lively. The author's enthusiasm and wit are obvious on almost every page and I recommend the text very strongly indeed.' Proceedings of the Edinburgh Mathematical Society

'This is a well-written, challenging introductory text that addresses the essential issues in the development of effective numerical schemes for the solution of differential equations: stability, convergence, and efficiency. The soft cover edition is a terrific buy - I highly recommend it.' Mathematics of Computation

'This book can be highly recommended as a basis for courses in numerical analysis.' Zentralblatt fur Mathematik

'The overall structure and the clarity of the exposition make this book an excellent introductory textbook for mathematics students. It seems also useful for engineers and scientists who have a practical knowledge of numerical methods and wish to acquire a better understanding of the subject.' Mathematical Reviews

'… nicely crafted and full of interesting details.' ITW Nieuws

'I believe this book succeeds. It provides an excellent introduction to the numerical analysis of differential equations . . .' Computing Reviews

'As a mathematician who developed an interest in numerical analysis in the middle of his professional career, I thoroughly enjoyed reading this text. I wish this book had been available when I first began to take a serious interest in computation. The author's style is comfortable . . . This book would be my choice for a text to 'modernize' such courses and bring them closer to the current practice of applied mathematics.' American Journal of Physics

'Iserles has successfully presented, in a mathematically honest way, all essential topics on numerical methods for differential equations, suitable for advanced undergraduate-level mathematics students.' Georgios Akrivis, University of Ioannina, Greece

'The present book can, because of the extension even more than the first edition, be highly recommended for readers from all fields, including students and engineers.' Zentralblatt MATH

Editorial Reviews

'A well written and exciting book … the exposition throughout is clear and very lively. The author's enthusiasm and wit are obvious on almost every page and I recommend the text very strongly indeed.' Proceedings of the Edinburgh Mathematical Society

'This is a well-written, challenging introductory text that addresses the essential issues in the development of effective numerical schemes for the solution of differential equations: stability, convergence, and efficiency. The soft cover edition is a terrific buy - I highly recommend it.' Mathematics of Computation

'This book can be highly recommended as a basis for courses in numerical analysis.' Zentralblatt fur Mathematik

'The overall structure and the clarity of the exposition make this book an excellent introductory textbook for mathematics students. It seems also useful for engineers and scientists who have a practical knowledge of numerical methods and wish to acquire a better understanding of the subject.' Mathematical Reviews

'… nicely crafted and full of interesting details.' ITW Nieuws

'I believe this book succeeds. It provides an excellent introduction to the numerical analysis of differential equations . . .' Computing Reviews

'As a mathematician who developed an interest in numerical analysis in the middle of his professional career, I thoroughly enjoyed reading this text. I wish this book had been available when I first began to take a serious interest in computation. The author's style is comfortable . . . This book would be my choice for a text to 'modernize' such courses and bring them closer to the current practice of applied mathematics.' American Journal of Physics

'Iserles has successfully presented, in a mathematically honest way, all essential topics on numerical methods for differential equations, suitable for advanced undergraduate-level mathematics students.' Georgios Akrivis, University of Ioannina, Greece

'The present book can, because of the extension even more than the first edition, be highly recommended for readers from all fields, including students and engineers.' Zentralblatt MATH

From the Publisher