Synopses & Reviews
This is the only book on spectral methods built around "Matlab" programs. Along with finite differences and 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.
Table of Contents
Preface; 1. Differentiation matrices; 2. Unbounded grids: the semidiscrete Fourier transform; 3. Periodic grids: the DFT and FFT; 4. Smoothness and spectral accuracy; 5. Polynomial interpolation and clustered grids; 6. Chebyshev differentiation matrices; 7. Boundary value problems; 8. Chebyshev series and the FFT; 9. Eigenvalues and pseudospectra; 10. Time-stepping and stability regions; 11. Polar coordinates; 12. Integrals and quadrature formulas; 13. More about boundary conditions; 14. Fourth-order problems; Afterword; Bibliography; Index.