The recently developed distributed approximating function (DAF) method for evaluating the action of the kinetic energy evolution operator, and the kinetic energy portion of the Hamiltonian, is applied to treat collinear reactive scattering. The DAF approach yields highly banded representations of these operators, while permitting the relevant matrix-vector multiplications to be done by fast convolution. Both time-dependent and time-independent wavepacket propagation schemes are employed, along with the DAFs, and accurate results obtained far the standard H + H-2 collinear reactive scattering system.