Sharp error bounds for the derivatives of Lidstone-spline interpolation II

Abstract In this paper, we shall derive explicit error estimates in L ∞ norm between a given function f ( x ) ∈ PC ( n ) [ a , b ], 4 ≤ n ≤ 6 and its quintic Lidstone-spline interpolate. The results obtained are then used to establish precise error bounds for the approximated and biquintic Lidstone-spline interpolates. We also include applications to integral equations and boundary value problems as well as sufficient numerical examples which dwell upon the sharpness of the obtained results.

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