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

We derive ε -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, ε 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 ε -uniform convergence and indicates the convergence behaviour for such grids. Numerical results are presented which confirm the ε -uniform convergence rates.