The Analysis of Lagrange Interpolation for Functions with a Boundary Layer Component

摘要

Interpolation formulas for the functions of one variable with a boundary layer component are investigated. An interpolated function corresponds to a solution of a singular perturbed problem. An application of Lagrange interpolation on a uniform mesh leads to significant errors. Two approaches for a interpolation of a function with a boundary layer component are considered: a fitting of the interpolation formula to a boundary layer component and the application of Lagrange interpolation on Shishkin mesh. Numerical results are discussed.