In this paper, we are concerned with a problem of computing differentiation matrices for the approximation of high-order derivatives of functions defined on general non-tensor domains. For that purpose, given any two-dimensional domain, we develop a process for constructing collocation points with well conditioned corresponding Vandermonde matrix. Afterward, we give an algorithm for computing differentiation matrices via pseudo-spectral methods using these collocation points. The L²-norm of approximation errors are then analyzed through some numerical examples.

Lebesgue constant, high-order interpolation, pseudo spectral collocation methods, non-tensorial domains, differentiation matrices.