Geodesic
Spline interpolation on a uniform grid for a function with a boundary layer component
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 2, pp. 221-233

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Spline interpolation of functions of one variable with a boundary-layer component is examined. Functions of this type can arise in the solution of a singularly perturbed boundary value problem on an interval. Spline interpolation formulas that are exact for the boundary-layer component are constructed, and their errors are estimated. Formulas for calculating the derivative based on the constructed interpolants are obtained. Numerical results are presented. 
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     author = {A. I. Zadorin and N. A. Zadorin},
     title = {Spline interpolation on a uniform grid for a function with a boundary layer component},
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A. I. Zadorin; N. A. Zadorin. Spline interpolation on a uniform grid for a function with a boundary layer component. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 2, pp. 221-233. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_2_a1/