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Spectral Methods in MATLAB

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by Lloyd N. Trefethen


2000 / xviii + 165 pages / Softcover / ISBN: 978-0-898714-65-4 / List Price $62.00 / SIAM Member Price $43.40 / Order Code SE10

"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, Ford Foundation Professor of Applied Mathematics, Brown University

"Fascinating mathematics, intriguing graphics, and beautiful MATLAB codes." – Cleve Moler, Chairman and Chief Scientist, The MathWorks, Inc.

"I used this book to teach a summer school course in computational aspects and applications of spectral methods in Denmark during the summer of 2000. The success of the course was due quite significantly to this book, which made it very easy for the students to get started on some computations and get their hands wet from the first day.

I mainly used the text as the central reference throughout the course combined with a couple of additional standard references. During the mornings I went through some of the missing theory while students solved small problems using MATLAB during the afternoon.

The book provided inspiration in addition to being a source of working computational examples. Students enjoyed the problem solving sessions and were actually capable of developing projects of their own interest after less than a week.

I am certain the book will be a success and hopefully will help promote the use of spectral methods beyond a small clan of people by convincingly showing that the main myth of spectral methods—that they are difficult—is indeed incorrect!" – Jan S. Hesthaven, Brown University

"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, Applied Mathematics Instructor Department of Mathematics, Massachusetts Institute of Technology

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.

Users of this book include advanced undergraduate and graduate students studying numerical methods for PDEs, numerical analysts, engineers, and computationally oriented physical scientists in all areas. The reader must have reasonable exposure to linear algebra, PDEs at the practical (not theoretical) level, and MATLAB.

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

ISBN: 9780898714654

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