  Three different numerical techniques for solving a coupled channel
Schroedinger equation are compared. This benchmark equation, which describes
the collision between two ultracold atoms, consists of two channels, each
containing the same diagonal Lennard-Jones potential, one of positive and the
other of negative energy. The coupling potential is of an exponential form. The
methods are i) a recently developed spectral type integral equation method
based on Chebyshev expansions, ii) a finite element expansion, and iii) a
combination of an improved Numerov finite difference method and a Gordon
method. The computing time and the accuracy of the resulting phase shift is
found to be comparable for methods i) and ii), achieving an accuracy of ten
significant figures with a double precision calculation. Method iii) achieves
seven significant figures. The scattering length and effective range are also
obtained.
