AbstractAn initial-boundary value problem is considered in an unbounded do-
main on the x-axis for a singularly perturbed parabolic reaction-diffusion equation. For small values of the
parameter ε, a parabolic boundary layer arises in a neighbourhood of the lateral part
of the boundary. In this problem, the error of a discrete solution in the maximum
norm grows without bound even for fixed values of the parameter ε. In
the present paper, the proximity of solutions of the initial-boundary value problem
and of its numerical approximations is considered. Using the method of special grids condensing
in a neighbourhood of the boundary layer, a special finite difference scheme converging
ε-uniformly in the weight maximum norm has been constructed.
Initial boundary value problem for the singularly perturbed Boussinesq-type equation
