Interpolation Hermite method

Each of the methods described under rendering above can be applied directly to evaluation. The third, Hermite, form is probably most relevant to applications requiring high accuracy. In fact where the second derivative can also be evaluated exactly at dyadic points, a quintic Hermite interpolant can be used to give an even higher rate of approximation. 

The coefficients are compnted from (4.138) by substimting the Hermite interpolation polynomial (4.134) into the update formula (4.130). An efficient implementation of BDF methods is presented below in the discnssion of DAE systems. For the test equation jc = Ax, Ah> = we again expand the states in the numerical trajectory in eigenvectors of A, and define the growth coefficient for each mode as... 

FIGURE 12.17 Comparison of Weibull extreme distribution function (—) and Hermite interpolation method (-) for representing experimental distillation data of products from hydrocracking at different temperatures ( ) 410°C, ( ) 430°C, and (A) 450°C. (Data from El-Kady, F.Y., Indian J. TechnoL, 17, 176, 1979.)... 

---