Spectral Methods in MATLAB

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.

This is the only book on spectral methods built around MATLAB programs. This hands-on introduction is built around forty short and powerful MATLAB programs, easily adaptable to the reader's own needs, and which can also be downloaded from the internet. Key ideas are presented alongside many figures and examples.