Nodes difference method in Hermite interpolation problem solving

This paper discusses three methods of Hermite interpolation problem solving,the method of basis function to solve Lagrange polynomial interpolation,Newton interpolation function method,and the nodes difference method.Three methods are compared using specific examples.In the method of basis function to solve Lagrange polynomial interpolation,all pending functions need to be re-calculated which is very complex without a uniform formula.The methods of Newton interpolation function and the nodes difference to get the remainder of the two-point cubic Hermite interpolation require simpler calculation without remembering particular formula,and can be proved to get quickly and easily the error limit of the piecewise cubic Hermite interpolation.