ON INTERPOLATION of FUNCTIONS with a BOUNDARY LAYER BY CUBIC SPLINES
نویسندگان
چکیده
The problem of article is cubic spline-interpolation of functions having high gradient regions. It is shown that uniform grids are inefficient to be used. In case of piecewise-uniform grids, concentrated in the boundary layer, for cubic spline interpolation are announced asymptotically exact estimates on a class of functions with an exponential boundary layer. There are obtained results showing divergent in small parameter estimates and divergence of interpolation processes. The modified cubic spline with uniform in small parameter interpolation error is offered. The results of numerical experiments confirming theoretical estimates are given.
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