Convergence Analysis of Finite-Difference Approximations of an Inhomogeneous Singularly Perturbed Boundary Value Problem Using Grid Equidistribution.

Convergence analysis of nite-diierence approximations of an inhomogeneous singularly perturbed boundary value problem using grid equidistribution. We derive-uniform error estimates for two rst-order upwind discretisations of a model inhomogeneous, second-order, singularly perturbed boundary value problem on a non-uniform grid. Here, 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 oor and a power of the second derivative of the solution. Analysis shows how the oor should be chosen to ensure-uniform convergence. The use of equidistribution principles appears in many grid adaption schemes and our analysis indicates the convergence behaviour on such grids. Numerical results are given that connrm the-uniform convergence rates.