Error estimation for a numerical solution to a boundary value problem with a boundary layer (Q1975100)

The paper is devoted to a boundary value problem for a second-order ordinary differential equation with a small parameter at the highest-order derivative and moderately smooth coefficients. A method for solving this problem on a nonuniform grid condensing in a boundary layer is analyzed. An optimal error estimate that is uniform with respect to the parameter is obtained for a numerical solution. The analysis is essentially based on transition to a close problem with smooth coefficients.