Differentiation and Numerical Integral of the Cubic Spline Interpolation

Based on analysis of cubic spline interpolation, the differentiation formulas of the cubic spline interpolation on the three boundary conditions are put up forward in this paper. At last, this calculation method is illustrated through an example. The numerical results show that the spline numerical differentiations are quite effective for estimating first and higher derivatives of equally and unequally spaced data. The formulas based on cubic spline interpolation solving numerical integral of discrete function are deduced. The degree of integral formula is n=3.The formulas has high accuracy. At last, these calculation methods are illustrated through examples.