Sinopsis
The Matlab programs in this book are terse. I have tried to make each one compact enough to t on a single page, and most often, on half a page. Of course, there is a message in this style, which is the message of this book: you can do an astonishing amount of serious computing in a few inches of computer code! And there is another message, too. The best discipline for making sure you understand something is to simplify it, simplify it relentlessly. Without a doubt, readability is sometimes impaired by this obsession with compactness. For example, I have often combined two or three short Matlab commands on a single program line. You may prefer a looser style, and that is ne. What's best for a printed book is not necessarily what's best for one's personal work.
Another idiosyncrasy of the programming style in this book is that the structure is at: with the exception of a crucial function cheb de ned in Chapter 6 and used repeatedly thereafter, I make almost no use of functions. (Three further functions chebfft, clencurt, and gauss are introduced in Chapters 8 and 12, but each is used just locally.) This style has the virtue of emphasizing how much can be achieved compactly, but as
Content
- Di erentiation Matrices
- Unbounded Grids: The Semi-Discrete Fourier Transform
- Periodic Grids: The DFT and FFT
- Smoothness and Spectral Accuracy
- Polynomial Interpolation and Clustered Grids
- Chebyshev Di erentiation Matrices
- Boundary Value Problems
- Chebyshev Series and the FFT
- Eigenvalues and Pseudospectra
- Time-Stepping and Stability Regions
- Polar Coordinates
- Integrals and Quadrature Formulas
- More About Boundary Conditions
- Fourth-Order Problems
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