Hello all,
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.
You can transform to a arbitary interval by a linear transformation of the form x=(b-a)/2*t+(b+a)/2, where x is in [a,b] and t in [-1,1]. It should then be straightforward to derive the corresponding derivation formula for the interval [a,b] by using the chain rule. But, without having the expression you are referring to for the differential operator I cannot help you more.
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