We investigate the performance of a scattering algorithm which uses purely real algebra for the major part of the wave function calculation, while incorporating automatically the appropriate boundary conditions. The algorithm falls in the category of time-independent wave packet methods ([R. Kosloff, J, Phys. Chem, 92, 2087 (1988)], and, more specifically for scattering [Y. Huang, W. Zhu, D. J. Kouri, and D. K. Hoffman, Chem, Phys. Lett, 206, 96 (1993)]), and combines two previous approaches : A method [V. A. Mandelshtam and H. S. Taylor, J. Chem. Phys. 103, 2903 (1995)] in which the action of the absorbing potentials is implicitly inserted in a polynomial expansion of the Green’s function, and a real initial wave function approach, in which zero initial momenta are avoided, Compared to the conventional, multiple time-step Chebyshev method, the new algorithm required three times less Hamiltonian evaluations for a model problem involving direct scattering. The new method also showed faster convergence for a problem involving resonances. Both, methods showed convergence problems in the vicinity of a very narrow resonance.