STABILITY OF A 3-POINT SCHEME FOR LINEAR 2ND-ORDER SINGULARLY PERTURBED BVPS WITH TURNING-POINTS

In this paper, we study stability properties of a numerical method applied to linear second order perturbed boundary-value problems with boundary or interior layers. The method consists of a three-point difference scheme with variable stepsize, the stability of which may be investigated by studying that of an LU factorization for the coefficient matrix of a suitable tridiagonal system. We also propose a mesh selection strategy, for treating boundary and interior layers, which furnishes a good mesh on which the three-point scheme is stable.