The numerical problems within analytical methods of solution for cubic equations of state

Abstract

It is possible to solve analytically cubic equations of state when they are reduced to a polynomial form, but it is knownthat at certain conditions application of the Cardano-Vieta formulas can produce wrong liquid density results due tonumerical errors. In this work the same behavior was found in the hybrid analytical-iterative Deiters solution method,the causes of the errors were revisited, and for each method a new criterion was proposed to stop the calculation whenwrong results can be produced. But it was also found that the wrong results can be avoided either using the reduceddensity as variable in the polynomial associated to the equation of state; or calculating the complete set of polynomialroots with the Jenkins-Traub algorithm, which can be even more advisable than any of the two aforementionedmethods.