Homotopic parametric continuation method for determining stationary states of chemical reactors with dispersion
Authors:
- Marek Berezowski,
- Marcin Lawnik
Abstract
Physical processes occurring in devices with distributed variables and a turbulent tide with a dispersion of mass and heat are often modeled using systems of nonlinear equations. Solving such a system is sometimes impossible in an analytical manner. The iterative methods, such as Newton’s method, are not always sufficiently effective in such cases. In this article, a combination of the homotopy method and the parametric continuation method was proposed to solve the system of nonlinear differential equations. These methods are symmetrical, i.e., the calculations can be made by increasing or decreasing the value of the parameters. Thanks to this approach, the determination of all roots of the system does not require any iterative method. Moreover, when the solutions of the system are close to each other, the proposed method easily determines all of them. As an example of the method use a mathematical model of a non-adiabatic catalytic pseudohomogeneous tubular chemical reactor with longitudinal dispersion was chosen.
- Record ID
- CUTd7682609e5f54360bd59daa5fb42945c
- Publication categories
- ;
- Author
- Journal series
- Symmetry, ISSN , e-ISSN 2073-8994, Monthly
- Issue year
- 2021
- Vol
- 13
- No
- 12
- Pages
- [1-7]
- Article number
- 2324
- Other elements of collation
- wykr.; Bibliografia (na s.) - 6-7; Bibliografia (liczba pozycji) - 18; Oznaczenie streszczenia - Abstr.; Numeracja w czasopiśmie - Vol. 13, Iss. 12, Spec. Iss.
- Substantive notes
- Special Issue: Chaotic Systems and Nonlinear Dynamics
- Keywords in English
- pseudohomogeneous catalytic tubular chemical reactor, dispersion, multiple stationary states, homotopy method, parametric continuation method
- DOI
- DOI:10.3390/sym13122324 Opening in a new tab
- URL
- https://www.mdpi.com/2073-8994/13/12/2324 Opening in a new tab
- Language
- eng (en) English
- License
- Score (nominal)
- 70
- Publication indicators
- = 2
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUTd7682609e5f54360bd59daa5fb42945c/
- URN
urn:pkr-prod:CUTd7682609e5f54360bd59daa5fb42945c
* presented citation count is obtained through Internet information analysis, and it is close to the number calculated by the Publish or PerishOpening in a new tab system.