Cubic Spline on a Bakhvalov Mesh in the Presence of a Boundary Layer

Abstract

AbstractThe problem of cubic spline interpolation on the Bakhvalov mesh of functions with region of large gradients is considered. Asymptotically accurate two-side error estimates are obtained for a class of functions with an exponential boundary layer. It is proved that the error estimates of traditional spline interpolation are not uniform in a small parameter, and the error itself can increase indefinitely when the small parameter tends to zero at a fixed number of nodes N. A modified cubic spline is proposed for which uniform estimates of the order O(N −4) have been experimentally confirmed.