Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations is a 325-page textbook which was written during 1985-1994 and used in graduate courses at MIT and Cornell on the numerical solution of partial differential equations.
The book has not been completed, though half of it got expanded into Spectral Methods in MATLAB. Nevertheless, the part of it that is written is in quite polished form, including many exercises, and is suitable for classroom use (and indeed has been used at quite a few universities). Copies are now available here for use by anyone who wishes. There is no restriction on this use, except that any copies must not alter the original text and must include the author’s name.
The files currently online are missing some tables, figures, and text that are not available in PostScript or are in copyright; a list of some of these omissions is available.
Thanks to Darryl Yong of Harvey Mudd College for converting these PostScript files into searchable pdf files.
Cover Pages (ps,pdf)
Chapter 1. Ordinary differential equations. (pdf)
Chapter 2. Fourier analysis. (pdf)
Chapter 3. Finite difference approximations. (pdf)
Chapter 4. Accuracy, stability and convergence. (pdf)
Chapter 5. Dissipation, dispersion, and group velocity. (pdf)
Chapter 6. Boundary conditions. (pdf)
Chapter 7. Fourier spectral methods. (pdf)
Chapter 8. Chebyshev spectral methods. (pdf)
References. (pdf)
A reasonable way to cite this book would be: Lloyd N. Trefethen, Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations, unpublished text, 1996, available at http://people.maths.ox.ac.uk/trefethen/pdetext.html