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

AbstractIn 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