A numerical method is given for affecting nonlinear Schrodinger evolution o
n an initial wave function, applicable to a wide range of problems, such as
time-dependent Hartree, Hartree-Fock, density-functional, and Gross-Pitaev
skii theories. The method samples the evolving wave function at Chebyshev q
uadrature points of a given Lime interval. This achieves an optimal degree
of representation. At these sampling points, an implicit equation, represen
ting an integral Schrodinger equation, is given for the sampled wave functi
on. Principles and application details are described, and several examples
and demonstrations of the method and its numerical evaluation on the Gross-
Pitaevskii equation for a Bose-Einstein condensate are shown.