  We show in this paper that third- and fourth-order low storage Runge-Kutta
algorithms can be built specifically for quadratic nonlinear operators, at the
expense of roughly doubling the time needed for evaluating the temporal
derivatives. The resulting algorithms are especially well suited for
computational fluid dynamics. Examples are given for the H\'enon-Heiles
Hamiltonian system and, in one and two space dimensions, for the Burgers
equation using both a pseudo-spectral code and a spectral element code,
respectively. The scheme is also shown to be practical in three space solving
the incompressible Euler equation using a fully parallelized pseudo-spectral
code.
