A First Course in the Numerical Analysis of Differential Equations

Preface to the first edition; Preface to the second edition; Flowchart of contents; Part I. Ordinary differential equations: 1. EulerâEUR(TM)s method and beyond; 2. Multistep methods; 3. RungeâEUR"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. BlufferâEUR(TM)s guide to useful mathematics: A.1. Linear algebra; A.2. Analysis; Bibliography; Index.

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.

'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