  Classical Density Functional Theory (DFT) is a statistical-mechanical
framework to analyze fluids, which accounts for nanoscale fluid inhomogeneities
and non-local intermolecular interactions. DFT can be applied to a wide range
of interfacial phenomena, as well as problems in adsorption, colloidal science
and phase transitions in fluids. Typical DFT equations are highly non-linear,
stiff and contain several convolution terms. We propose a novel, efficient
pseudo-spectral collocation scheme for computing the non-local terms in real
space with the help of a specialized Gauss quadrature. Due to the exponential
accuracy of the quadrature and a convenient choice of collocation points near
interfaces, we can use grids with a significantly lower number of nodes than
most other reported methods. We demonstrate the capabilities of our numerical
methodology by studying equilibrium and dynamic two-dimensional test cases with
single- and multispecies hard-sphere and hard-disc particles modelled with
fundamental measure theory, with and without van der Waals attractive forces,
in bounded and unbounded physical domains. We show that our results satisfy
statistical mechanical sum rules.
