  We suggest a pseudospectral method for solving the three-dimensional
time-dependent Gross-Pitaevskii (GP) equation and use it to study the resonance
dynamics of a trapped Bose-Einstein condensate induced by a periodic variation
in the atomic scattering length. When the frequency of oscillation of the
scattering length is an even multiple of one of the trapping frequencies along
the $x$, $y$, or $z$ direction, the corresponding size of the condensate
executes resonant oscillation. Using the concept of the differentiation matrix,
the partial-differential GP equation is reduced to a set of coupled ordinary
differential equations which is solved by a fourth-order adaptive step-size
control Runge-Kutta method. The pseudospectral method is contrasted with the
finite-difference method for the same problem, where the time evolution is
performed by the Crank-Nicholson algorithm. The latter method is illustrated to
be more suitable for a three-dimensional standing-wave optical-lattice trapping
potential.
