Spectral Methods in MATLAB

This is the only book on spectral methods built around MATLAB programs.

Lloyd N. Trefethen (Author)

9780898714654, Society for Industrial and Applied Mathematics

Paperback / softback, published 1 July 2000

183 pages
25.4 x 17.6 x 1 cm, 0.34 kg

'The book's succinct style and the understanding that is gained by parsing and experimenting with MATLAB routines allow for a large number of fundamental concepts to be conveyed in a few pages… I recommend this book highly; it is clear, concise, and dense with interesting and exciting examples. It is an appropriate text for an introductory class on the subject and also includes many ideas and explanations that are appealing to a broader research audience.' SIAM Review

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.

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.

Subject Areas: Mathematical & statistical software [UFM], Applied mathematics [PBW], Numerical analysis [PBKS]