The numerical problems within analytical methods of solution for cubic equations of state
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| Format: | Artículo científico |
| Language: | en |
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Universidad del Valle
2012
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| author | Javier I. Carrero-Mantilla |
| author_facet | Javier I. Carrero-Mantilla |
| contents | The numerical problems within analytical methods of solution for cubic equations of state Javier I. Carrero-Mantilla Ingeniería Cardano Vieta method Polynomial roots Cubic equations of state It is possible to solve analytically cubic equations of state when they are reduced to a polynomial form, but it is known that at certain conditions application of the Cardano-Vieta formulas can produce wrong liquid density results due to numerical 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 when wrong results can be produced. But it was also found that the wrong results can be avoided either using the reduced density as variable in the polynomial associated to the equation of state; or calculating the complete set of polynomial roots with the Jenkins-Traub algorithm, which can be even more advisable than any of the two aforementioned methods. 2012 artículo científico 0123-3033 https://www.redalyc.org/articulo.oa?id=291323571007 en http://www.redalyc.org/revista.oa?id=2913 Ingeniería y Competitividad application/pdf Universidad del Valle Ingeniería y Competitividad (Colombia) Num.1 Vol.14 |
| format | Artículo científico |
| id | redalyc_291323571007 |
| institution | Redalyc |
| language | en |
| publishDate | 2012 |
| publisher | Universidad del Valle |
| spellingShingle | The numerical problems within analytical methods of solution for cubic equations of state Javier I. Carrero-Mantilla Ingeniería Cardano Vieta method Polynomial roots Cubic equations of state The numerical problems within analytical methods of solution for cubic equations of state Javier I. Carrero-Mantilla Ingeniería Cardano Vieta method Polynomial roots Cubic equations of state It is possible to solve analytically cubic equations of state when they are reduced to a polynomial form, but it is known that at certain conditions application of the Cardano-Vieta formulas can produce wrong liquid density results due to numerical 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 when wrong results can be produced. But it was also found that the wrong results can be avoided either using the reduced density as variable in the polynomial associated to the equation of state; or calculating the complete set of polynomial roots with the Jenkins-Traub algorithm, which can be even more advisable than any of the two aforementioned methods. 2012 artículo científico 0123-3033 https://www.redalyc.org/articulo.oa?id=291323571007 en http://www.redalyc.org/revista.oa?id=2913 Ingeniería y Competitividad application/pdf Universidad del Valle Ingeniería y Competitividad (Colombia) Num.1 Vol.14 |
| title | The numerical problems within analytical methods of solution for cubic equations of state |
| topic | Ingeniería Cardano Vieta method Polynomial roots Cubic equations of state |
| url | https://www.redalyc.org/articulo.oa?id=291323571007 |