  A Dirichlet problem is considered for the eikonal equation in an anisotropic
medium. The nonlinear boundary value problem (BVP) formulated in the present
work is the limit of the diffusion-reaction problem with a reaction parameter
tending to infinity. To solve numerically the singularly perturbed
diffusion-reaction problem, monotone approximations are employed. Numerical
examples are presented for a two-dimensional BVP for the eikonal equation in an
anisotropic medium. The standard piecewise-linear finite-element approximation
in space is used in computations.
