A First Course in the Numerical Analysis of Differential Equations: 44 (Cambridge Texts in Applied Mathematics, Series Number 44)
Cambridge University Press
Edition: 2, 1/1/2009
EAN 9780521734905, ISBN10: 0521734908
Paperback, 480 pages, 24.4 x 17.5 x 2.5 cm
Language: English
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.
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.
'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 '