Are there any alterations for the Chebyshev Differentiation Matrices on an arbitrary domain [a,b]?

Question

I'm implementing the Chebyshev collocation method for solving PDEs, more specifically the shallow water equations. I know the Chebyshev differentiation matrices (or differential operators) are, for default, for functions defined on the domain [-1,+1], which is a characteristic of the Chebyshev polynomials. My question is: if I want to evaluate the derivatives on an arbitrary domain [a,b], which alterations should I carry on the Chebyshev differentiation matrices? I looked out for this on the Trefethen's book "Spectral Methods in Matlab", but haven't found any mentions to this issue. Thanks in advance.

Answer 1

I currently use the Chebyshev differentiation matrices and the Weideman & Reddy Matlab package to obtain them.

In their paper, http://dl.acm.org/citation.cfm?doid=365723.365727, they rescale the domain $[a,b]$ to $[-1,+1]$ with a simple linear transformation.

I would suggest you to do the same to your data, apply any differentiation, and then scale back to your original domain.