Caillaud-Padmanabhan method

One of the most successful methods is the Michelsen method, obtained as a small variant on the Caillaud-Padmanabhan method (Chan et al., 1978) ... 

Michelsen s third order semi-implicit Runge-Kutta method is a modified version of the method originally proposed by Caillaud and Padmanabhan (1971). This third-order semi-implicit method is an improvement over the original version of semi-implicit methods proposed in 1963 by Rosenbrock. 

Caillaud, J.B., and L. Padmanabhan, An Improved Semi-Implicit Runge-Kutta Method for Stiff Systems, Chem. Eng. J. 2, 22 -2i2 (1971). 

The last part of the process is now to solve (integrate) the equation system 5.129. We could use the simple Runge-Kutta method, probably going to a fourth-order scheme since we (hopefully) are not limited here by the second-order discretisation error inherent in system 5.13. it is more common to employ a more sophisticated technique. Whiting and Carr (1977) suggest Hamming s modified predictor-corrector method, Villadsen and Michelsen (1978) that of Caillaud and Padmanabhan (1971) (and provide the actual subroutines). There are other methods. The criterion will always... 

Caillaud JB, Padmanabhan L (1971) An improved semi-implicit Runge-Kutta method for stiff systems. Chem Eng J 2 227. 

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