Typically Chebyshev interpolation from $-1$ to $1$ with angle from $0$ to $\pi$:

  • $\xi_j=\cos \left ({\pi j \over N}\right )$
  • $x_j=(1+\xi_j) * {L \over 2}$
  • $w$:
    • $w_0=\pi/(2N)$
    • $w_{1,...,N-1}=\pi/(N)$
    • $w_N=\pi/(2N)$

I appear to have a need in the same with angle from $0$ to $\pi/2$ only, while solving a collocation grid problem where mesh is very fine inside of the computational domain and gets coarser near computational domain boundary. Literature review does not appear to be fruitful.

  • 3
    $\begingroup$ Can you not simply map the input angles to the appropriate range by multiplying by 2? If that's not the solution, you may need to explain more carefully. $\endgroup$ – Bill Barth Jan 3 '14 at 16:41
  • 3
    $\begingroup$ The standard practice is to map whatever computational domain you have to [-1,1]. So if you have $f(t), t \in [0, 1]$, just do $f(g(t)), g(t) = \frac{t+1}{2}$. $\endgroup$ – Jay Lemmon Jan 4 '14 at 18:04
  • $\begingroup$ This question is poorly written with no prior research. I'm surprised how you people manage to like it. (Mapping is indeed the working solution.) $\endgroup$ – user5273 Jan 31 '14 at 3:04

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