  A class of quasilinear singularly perturbed boundary value problems with a
turning point of attractive type is considered. The problems are solved
numerically by a finite-difference scheme on a special discretization mesh
which is dense near the turning point. The scheme is a combination of the
standard central and midpoint schemes and is practically second-order accurate.
Pointwise accuracy is uniform in the perturbation parameter and, moreover, L1
errors decrease when the perturbation parameter tends to 0. This is achieved by
the use of meshes which generalize the piecewise equidistant Shishkin mesh. Two
particular types of meshes are considered and compared.
