Sharp error bounds for the derivatives of Lidstone-spline interpolation

AbstractIn this paper, we shall provide explicit error bounds for the derivatives of cubic and quintic Lidstone-spline interpolates in L∞ norm. These results are used to acquire precise error bounds for the derivatives of approximated quintic as well as bicubic and biquintic Lidstone-spline interpolates. Sufficient numerical illustration which dwells upon the sharpness and importance to boundary value problems and integral equations of the obtained results is also included