Analogue of Cubic Spline for Functions with Large Gradients in a Boundary Layer
The problem of spline interpolation of functions with large gradients in the boundary layer is studied. It is assumed that the function contains the known up to a factor boundary layer component responsible for the large gradients of this function in the boundary layer. A modification of the cubic spline, based on the fitting to the boundary layer component is proposed. The questions of existence, uniqueness and accuracy of such spline are investigated. Estimates of the interpolation error which are uniform with respect to a small parameter are obtained.
KeywordsFunction and boundary layer Uniform grid Generalized spline Interpolation Error estimation
Supported by the program of fundamental scientific researches of the SB RAS 1.1.3., project 0314-2019-0009.