Spectral Methods in Matlab, by Lloyd N. Trefethen

Contents

1 Dierentiation Matrices 12 Unbounded Grids: The Semi-Discrete Fourier Transform 93 Periodic Grids: The DFT and FFT 174 Smoothness and Spectral Accuracy 295 Polynomial Interpolation and Clustered Grids 416 Chebyshev Dierentiation Matrices 517 Boundary Value Problems 618 Chebyshev Series and the FFT 759 Eigenvalues and Pseudospectra 8710 Time-Stepping and Stability Regions 10111 Polar Coordinates 11512 Integrals and Quadrature Formulas 12513 More About Boundary Conditions 135viii Spectral Methods in MATLAB14 Fourth-Order Problems 145