I am using Tchebyshev discretization to solve a system of PDEs.
Usually, I map the Tchebyshev space($\xi$, from -1 to 1) to physical space ($x$, from 0 to L) using $$x = (\xi +1)*L/2$$
Now, I also want my grids to be clustered around some point($x_c$) in the domain. Is there any standard mapping that can achieve this?
Any suggestion/ reference to standard texts are greatly appreciated.