Abstract
The problem of interpolation of a one-variable function considered as a solution to a boundary value problem for an equation with a small parameter ɛ in the highest derivative is investigated. The application of a Lagrange polynomial for such a function on a uniform grid may result in serious errors. For a Shishkin grid, ɛ-uniform error estimates of Lagrange polynomial interpolation are obtained. The Shishkin grid is modified to increase the interpolation accuracy. For Newton-Cotes formulas on such grids, ɛ-uniform error estimates are obtained. The results of numerical experiments confirm the theoretical estimates.
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