Spectral Methods in Matlab,9780898714654

Spectral Methods in Matlab

by
ISBN13: 9780898714654
ISBN10: 0898714656
Format: Paperback
Pub. Date: 2000-07-01
Publisher(s): SOCIETY FOR INDUSTRIAL & APPLIED MA
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Summary

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.

Author Biography

Lloyd N. Trefethen is Professor of Numerical Analysis at Oxford University.

Table of Contents

Preface ix
Acknowledgments xiii
A Note on the MATLAB Programs xv
Differentiation Matrices
1(8)
Unbounded Grids: The Semidiscrete Fourier Transform
9(8)
Periodic Grids: The DFT and FFT
17(12)
Smoothness and Spectral Accuracy
29(12)
Polynomial Interpolation and Clustered Grids
41(10)
Chebyshev Differentiation Matrices
51(10)
Boundary Value Problems
61(14)
Chebyshev Series and the FFT
75(12)
Eigenvalues and Pseudospectra
87(14)
Time-Stepping and Stability Regions
101(14)
Polar Coordinates
115(10)
Integrals and Quadrature Formulas
125(10)
More about Boundary Conditions
135(10)
Fourth-Order Problems
145(8)
Afterword 153(2)
Bibliography 155(6)
Index 161

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