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(s): Lloyd Nicholas Trefethen
Publisher: SIAM
Year: 2000
Language: English
Pages: 186
Contents......Page 9
Preface......Page 11
Acknowledgments......Page 15
A Note on the MATLAB Programs......Page 17
1 Differentiation Matrices ......Page 21
2 Unbounded Grids: The Semidiscrete Fourier Transform ......Page 29
3 Periodic Grids: The DFT and FFT ......Page 37
4 Smoothness and Spectral Accuracy ......Page 49
5 Polynomial Interpolation and Clustered Grids ......Page 61
6 Chebyshev Differentiation Matrices ......Page 71
7 Boundary Value Problems ......Page 81
8 Chebyshev Series and the FFT ......Page 95
9 Eigenvalues and Pseudospectra ......Page 107
10 Time-Stepping and Stability Regions ......Page 121
11 Polar Coordinates ......Page 135
12 Integrals and Quadrature Formulas ......Page 145
13 More about Boundary Conditions ......Page 155
14 Fourth-Order Problems ......Page 165
Afterword......Page 173
Bibliography......Page 175
Index......Page 181
