This is the only book on spectral methods built around MATLAB programs. Along with finite differences and finite elements, spectral methods are one of the three main technologies for solving partial differential equations on computers. Since spectral methods involve significant linear algebra and graphics they are very suitable for the high level programming of MATLAB. This hands-on introduction is built around forty short and powerful MATLAB programs, which the reader can download from the World Wide Web. This book presents the key ideas along with many figures, examples, and short, elegant MATLAB programs for readers to adapt to their own needs. It covers ODE and PDE boundary value problems, eigenvalues and pseudospectra, linear and nonlinear waves, and numerical quadrature.
Rezensionen / Stimmen
A brief, intuitive, and excellent introductory textbook of spectral methods. Readers with basic experience of finite difference methods can easily get to the core knowledge of spectral methods through this book. Those MATLAB scripts for examples in the book are very useful for both teaching and research.""- Tzyy-Leng Allen Horng, Feng Chia University, Taiwan;
""This book is a very nice addition to the collection of books on spectral methods, from a totally different angle. It should attract more students and researchers to the powerful spectral methods.""- Chi-Wang Shu, Mathematics of Computation;
""What a great book! I sat down to read through it last month, and it's so inspiringly lean with such great examples that I can't resist using it this term for 18.336 [Numerical Methods for PDEs].""- Peter Mucha, Massachusetts Institute of Technology;
""This is a charming book, beautifully written, easy to understand without sacrificing accuracy. The idea of using MATLAB is brilliant and will appeal to the students and the other readers.""- David Gottlieb, Brown University;
""Fascinating mathematics, intriguing graphics, and beautiful MATLAB codes.""- Cleve Moler, Chairman and Chief Scientist, The MathWorks, Inc.;
""The book's succinct style and the understanding that is gained by parsing and experimenting with MATLAB routines allow for a large number of fundamental concepts to be conveyed in a few pages... I recommend this book highly; it is clear, concise, and dense with interesting and exciting examples. It is an appropriate text for an introductory class on the subject and also includes many ideas and explanations that are appealing to a broader research audience.""- SIAM Review
Reihe
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Produkt-Hinweis
Broschur/Paperback
Klebebindung
Maße
Höhe: 258 mm
Breite: 177 mm
Dicke: 12 mm
Gewicht
ISBN-13
978-0-89871-465-4 (9780898714654)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Lloyd N. Trefethen is Professor of Numerical Analysis at Oxford University, UK. His previous book, Numerical Linear Algebra (with David Bau, III) is one of SIAM's bestsellers.
Preface
Acknowledgments
A Note on the MATLAB Programs
Chapter 1: Differentiation Matrices
Chapter 2: Unbounded Grids: The Semidiscrete Fourier Transform
Chapter 3: Periodic Grids: The DFT and FFT
Chapter 4: Smoothness and Spectral Accuracy
Chapter 5: Polynomial Interpolation and Clustered Grids
Chapter 6: Chebyshev Differentiation Matrices
Chapter 7: Boundary Value Problems
Chapter 8: Chebyshev Series and the FFT
Chapter 9: Eigenvalues and Pseudospectra
Chapter 10: Time-Stepping and Stability Regions
Chapter 11: Polar Coordinates
Chapter 12: Integrals and Quadrature Formulas
Chapter 13: More About Boundary Conditions
Chapter 14: Fourth-Order Problems
Afterword
Bibliography
Index