  The time dependent complex Schr\"odinger equation with cubic nonlinearity is
solved by constructing differential quadrature algorithm based on sinc
functions. Reduction to a coupled system of real equations enables to approach
the space derivative terms by the proposed method. The resulted ordinary
differential equation system is integrated with respect to the time variable by
using a bunch explicit methods of lower and higher orders. Some initial
boundary value problems containing some analytical and non-analytical initial
data are solved for experimental illustrations. The computational errors
between the analytical and numerical solutions are measured by the discrete
maximum error norm in case the analytical solution exists. The two conserved
quantities are calculated by using the numerical results in all cases. The
matrix stability analysis is implemented to control the time step size.
