  In this study, we investigate atom--dimer scattering within the framework of
the hyperspherical method. The coupled channel Schr\"odinger equation is solved
using the R-matrix propagation technique combined with the smooth variable
discretization method. In the matching procedure, the asymptotic wave functions
are expressed in the rotated Jacobi coordinates. We apply this approach to the
elastic scattering $^{3}$He(T$\uparrow$) + $^{4}$He$_{2}$ and H$\uparrow$ +
H$\uparrow$Li processes. The convergence of the scattering length as a function
of the propagation distance is studied. We find that the method is reliable and
can provide considerable savings over previous propagators.
