Grid approximations to singularly perturbed parabolic equations with turning points (Q1603193)

Solutions of a singularly perturbed boundary value problem have a rather complicated behaviour in a neighbourhood of boundary and internal layers. The author considers a class of singularly perturbed parabolic equations with convective terms on a closed interval. The behaviour of the solution in a neighbourhood of the boundary \(x=0\) and the existence of a boundary layer as well as its decay character away from the boundary is determined by the sign of a function appearing in the equations under consideration. For this class of problems a uniformly convergent finite-difference scheme is constructed making use of the method of condensing grids in a neighbourhood of the boundary layers and the singularity of the solution.