Homotopic Parametric Continuation Method for Determining Stationary States of Chemical Reactors with Dispersion
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, ar...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-12-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/12/2324 |
| _version_ | 1797500306737594368 |
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| author | Marek Berezowski Marcin Lawnik |
| author_facet | Marek Berezowski Marcin Lawnik |
| author_sort | Marek Berezowski |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T03:00:54Z |
| format | Article |
| id | doaj.art-7352fb93cf644634abd28485e719a8ef |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T03:00:54Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-7352fb93cf644634abd28485e719a8ef2023-11-23T10:45:31ZengMDPI AGSymmetry2073-89942021-12-011312232410.3390/sym13122324Homotopic Parametric Continuation Method for Determining Stationary States of Chemical Reactors with DispersionMarek Berezowski0Marcin Lawnik1Faculty of Chemical Engineering and Technology, Cracow University of Technology, ul. Warszawska 24, 30-155 Kraków, PolandDepartment of Mathematics Applications and Methods for Artificial Intelligence, Faculty of Applied Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, PolandPhysical 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.https://www.mdpi.com/2073-8994/13/12/2324pseudohomogeneous catalytic tubular chemical reactordispersionmultiple stationary stateshomotopy methodparametric continuation method |
| spellingShingle | Marek Berezowski Marcin Lawnik Homotopic Parametric Continuation Method for Determining Stationary States of Chemical Reactors with Dispersion Symmetry pseudohomogeneous catalytic tubular chemical reactor dispersion multiple stationary states homotopy method parametric continuation method |
| title | Homotopic Parametric Continuation Method for Determining Stationary States of Chemical Reactors with Dispersion |
| title_full | Homotopic Parametric Continuation Method for Determining Stationary States of Chemical Reactors with Dispersion |
| title_fullStr | Homotopic Parametric Continuation Method for Determining Stationary States of Chemical Reactors with Dispersion |
| title_full_unstemmed | Homotopic Parametric Continuation Method for Determining Stationary States of Chemical Reactors with Dispersion |
| title_short | Homotopic Parametric Continuation Method for Determining Stationary States of Chemical Reactors with Dispersion |
| title_sort | homotopic parametric continuation method for determining stationary states of chemical reactors with dispersion |
| topic | pseudohomogeneous catalytic tubular chemical reactor dispersion multiple stationary states homotopy method parametric continuation method |
| url | https://www.mdpi.com/2073-8994/13/12/2324 |
| work_keys_str_mv | AT marekberezowski homotopicparametriccontinuationmethodfordeterminingstationarystatesofchemicalreactorswithdispersion AT marcinlawnik homotopicparametriccontinuationmethodfordeterminingstationarystatesofchemicalreactorswithdispersion |