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 N. Trefethen
Publisher: SIAM: Society for Industrial and Applied Mathematics
Year: 2000
Language: English
Pages: 177
1 title.pdf......Page 1
2 C1 differentiation matrices.pdf......Page 13
3 C2 unbounded grid, semi-discrete fourier transform.pdf......Page 21
4 C3 period grids, The DFT and FFT.pdf......Page 29
5 C4 smoothness and spectral accuracy.pdf......Page 41
6 C5 polynomial interpolation and clustered grids.pdf......Page 52
7 C6 chebyshev differentiation matrices.pdf......Page 62
8 C7 boundary value problems.pdf......Page 71
9 C8 chebyshev series and the FFT.pdf......Page 85
10 C9 eigenvalues and pseudospectra.pdf......Page 97
11 C10 time-stepping and stability regions.pdf......Page 111
12 C11 polar coordinates.pdf......Page 125
13 C12 integrals and quadrature formulas.pdf......Page 135
14 C13 more about boundary conditions.pdf......Page 145
15 C14 fourth-order problems.pdf......Page 155
16 afterword, bibliography, index.pdf......Page 163
17 inside cover.pdf......Page 176
