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Spectral Methods in MATLAB

Lloyd N. Trefethen (author)

ISBN: 9780898714654

Publication Date: Jul 2000

Format: Paperback

This is the only book on spectral methods built around MATLAB programs. This hands-on introduction is built around 40 short and powerful MATLAB programs, which are all available online. This book presents the key ideas along with many figures, examples, and short, elegant MATLAB programs for readers to adapt to their own needs.

Temporarily out of stock: usually despatched in 10-14 days

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  • Table of Contents
  • Author Biography
  • Customer Reviews
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.


"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
Pages 181
Dimensions 229 x 152
Date Published 31 Jul 2000
Publisher SIAM - Society for Industrial and Applied Mathematics
Series Software Environments and Tools
Series Part 10
Subject/s Applied mathematics   Business applications  
  • 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
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.

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