Convergence analysis of finite difference approximations on equidistributed grids to a singularly perturbed boundary value problem

We derive epsilon-uniform error estimates for two first-order upwind discretizations of a model inhomogeneous, second-order, singularly perturbed boundary value problem on a non-uniform grid. Here, epsilon is the small parameter multiplying the highest derivative term. The grid is suggested by the equidistribution of a positive monitor function which is a linear combination of a constant floor and a power of the second derivative of the solution. Our analysis shows how the floor should be chosen to ensure epsilon-uniform convergence and indicates the convergence behaviour for such grids. Numerical results are presented which confirm the epsilon-uniform convergence rates. (C) 2000 IMACS. Published by Elsevier Science B.V. All rights reserved.